The protesters have built barricades and occupied key road junctions, and want to replace the government with an unelected "People's Council".
The government has deployed 18,000 security personnel to maintain order.
Prime Minister Yingluck Shinawatra has offered to meet protest leaders to discuss potentially delaying the polls.
Protesters allege Ms Yingluck is a proxy for her brother, former Prime Minister Thaksin Shinawatra, who was ousted by the military in 2006 and is currently in self-imposed exile.
Thaksin-allied parties draw considerable support from rural voters and have won the last four elections.
By Jonathan HeadBBC News, Bangkok
It was all wearily familiar - the shrieking whistles, the colourful umbrellas, the rousing speeches and music from the stages, which had been moved overnight to block some of Bangkok's busiest intersections.
And there was a certain weariness visible among the protesters, now in their third month of street rallies. Not the same levels of energy I saw a month ago.
Nor do these loyal supporters of a movement largely defined by its hatred of Prime Minister Yingluck Shinawatra and her family really know what results to expect from their marathon protest. They know about the idea of an "appointed committee" to fix Thai politics, and they can all mouth the slogans "Reform Before Election", and "Shutdown Bangkok, Restart Thailand".
But, asked what would happen if the prime minister resigned, and her own substantial support base outside Bangkok were to refuse to accept this, no one had an answer. "Well, it doesn't matter, because we are going to win anyway", was one woman's hopeful answer.
The longer these debilitating protests continue, the more likely a dramatic, perhaps violent, showdown between the two irreconcilable sides of Thai politics.
Would that spark the much-rumoured military intervention? A coup still seems unlikely, and yet not impossible. The crowds on the street are just a part of a bigger game, involving bargaining and brinkmanship by leaders on all sides.
In a conversation with Anchalee Praireerat, one of the more hard-core protest leaders, she would not say exactly what she expected to happen. But she assured me it would all be over in three days, and that the protesters would win.
But the protesters claim the Thaksin-allied parties' populist policies have created a flawed democracy. The main opposition party is now boycotting the 2 February polls.
Anti-government demonstrators have called on Ms Yingluck - who has urged protesters to respect the democratic process and use the February elections to choose the next government - to step down.
Thailand's election commission has called for the vote to be postponed to May.
But this is unlikely to satisfy the protesters, who want the Shinawatra family to be purged from politics, and a two-year period without elections in which an appointed committee would reform Thailand's political system, the BBC's Jonathan Head in Bangkok reports.
At least eight people have been killed since the protests began late last year. On Saturday, at least seven people were injured when unknown gunmen opened fire on demonstrators at the main rally site in Bangkok.
On Sunday night, an unidentified gunman attacked demonstrators at a protest site, shooting at least one man, officials said.
Police said a gunman also fired shots at the opposition party headquarters in a separate incident, although no casualties were reported.
Thousands are reported to have turned out for Monday's demonstrations. Protesters say they intend to achieve what they are calling a shutdown of the capital.
Protester Darunee Suredechakul told AP news agency: "The government has to go. Reforms must be carried out."
"We don't want to see the same old corrupted politicians returning to power over and over again," she added.
Seven major intersections have been blocked by the anti-government protest movement, which has erected stages and piles of sandbags across the roads, the BBC's Jonathan Head reports.
The government says it wants life to continue as normal through the shutdown and has ordered extra trains to run on the mass transit system and provided thousands of additional parking places outside the city centre, our correspondent adds.
Protesters also plan to surround key ministries and cut off their power supply in a bid to prevent them from functioning. About 150 schools have been told to close.
The protesters say they will remain in place for several days - but say they will not target public transport or the airports, which were closed for several days by anti-Thaksin protesters in 2008.
Protest leader Suthep Thaugsuban, who was formerly a senior opposition party politician, described the movement as "a people's revolution".
Ms Yingluck was "no longer prime minister" in the eyes of the demonstrators, he told reporters on Monday.
The government says it is deploying 8,000 soldiers and 10,000 police to keep order.
The military - which has carried out several coups in the past - has refused to rule out another one. Some fear an escalation of violence could lead to a military intervention.
The government has so far worked to avoid confrontation with the protesters.
Ms Yingluck had "ordered all police and military personnel to exercise utmost restraint and not to use all kinds of weapons in handling the protesters", the deputy prime minister said.
The political unrest is the worst to hit Thailand since the protests of 2010, which were against a government led by the current opposition party and left more than 90 people, mostly civilian protesters, dead.
The current protests began in November after Thailand's lower house passed a controversial amnesty bill which critics said could allow Mr Thaksin to return without serving time in jail for a corruption conviction. The bill was later rejected by the Senate.
Thailand remains bitterly divided over Mr Thaksin, one of the most polarising characters in Thai politics.
He is deeply unpopular with urban and middle class voters, but commands strong support in the rural communities his policies helped, with thousands of villages in north-east Thailand calling themselves "red villages" to indicate their loyalty to his party.
Protesters are blocking roads in parts of the Thai capital, Bangkok, in a bid to oust the government before snap elections on 2 February.