After the bus explosion, huge blasts were heard in the Gaza Strip as the Israeli bombardment of the Palestinian territory continued.
Eleven people were killed in Gaza on Wednesday, the health ministry said.
Unnamed Palestinian officials told news agencies a ceasefire between Hamas and Israel would be announced within hours.
After eight days of exchanges of fire between Israel and Palestinian militants in Gaza, US Secretary of State Hillary Clinton and UN Secretary General Ban Ki-moon are now in Cairo for talks with the Egyptian president.
There were "many details to work out" before a ceasefire could be reached, Mr Ban warned.
By Kevin ConnollyBBC News, Tel Aviv
In the immediate aftermath of the  bus bombing, there was a palpable sense of shock hanging in the air around the scene.
Israel's largest city has seen nothing like this for six-and-a-half years.
One resident - when told that the news of the explosion broadcast from mosques in Gaza has been greeted with a sound of celebratory gunfire there - said that they need to celebrate this as some kind of victory because they have nothing else to offer but violence.
A police helicopter still circled overhead and there were roadblocks at many main junctions around the scene as police hunted for the bomber or bombers seen running away from the scene.
Paradoxically, the explosion and the waves of Israeli air raids on Gaza this morning do not necessarily mean that the search for a ceasefire is dead.
It may mean that both sides are sending a signal that if a deal is agreed, they will be reaching it from what they regard as a position of strength.
The search for a diplomatic solution reaches a critical phase this afternoon when US Secretary of State Hillary Clinton meets Egyptian President Mohammed Mursi - the only leader with effective lines of communication both to Israel and to Hamas.
Earlier, she and UN Secretary General Ban Ki-moon held talks in the West Bank with the Palestinian Authority President Mahmoud Abbas.
The US "strongly condemns" the bus bombing, Mrs Clinton said.
Militants fired more rockets at Israel, while Israel renewed its naval artillery bombardment of Gaza late on Wednesday.
Israeli Prime Minister Benjamin Netanyahu's spokesman Ofir Gendelman said on his Twitter account that the bus explosion in Tel Aviv was a "terrorist attack".
The Ichilov medical centre in Tel Aviv said that of the 28 injured, 10 had suffered "body injuries" - three of them serious - three received "moderate-light" injuries including shrapnel wounds and burns, and the remainder were suffering from "anxiety".
The bus was passing the military headquarters in the city at the time of the blast.
Police say they believe the blast was caused by a bomb and they are still searching for a suspect.
According to Israel's ministry of foreign affairs, the last bomb attack in Tel Aviv was in April 2006, when a suicide bombing on a restaurant killed 11.
Hamas, the Islamist movement which has governed Gaza since 2007, has praised the attack but has not said it was behind the blast.
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Celebratory gunfire reportedly rang out in Gaza when local radio relayed news of the attack.
BBC correspondents then reported a series of massive explosions in Gaza, in an apparent Israeli strike on the sports stadium. Reports from Gaza say the stadium has in the past been used as a site to launch rockets.
Among the casualties on Wednesday was a six-year-old boy.
The health ministry in Gaza says a doctor at the Shifa hospital was called to treat the boy. When he reached the patient, he found it was his own son and the boy was dead, the health ministry said.
This is the eighth day of the current flare-up in violence between Israel and militants in Gaza.
Some 152 Palestinians and five Israelis have been killed, officials say.
In other developments:
Other sites hit in Gaza included a banker's villa, tunnels to Egypt used by smugglers and a media office, said to be linked to Hamas, that was situated two floors above the Agence France-Presse office in Gaza City.
Earlier, the IDF said 62 rockets fired by militants from Gaza had hit Israel on Wednesday, while another 20 were intercepted by its Iron Dome missile defence system.
The latest violence will further complicate ceasefire discussions taking place in the region.
In the West Bank, Mr Ban expressed "profound concern" at the civilian casualties in Gaza and also called on militants to end immediately their "indiscriminate attacks on Israeli population centres".
Mrs Clinton held talks with Israeli PM Benjamin Netanyahu in Jerusalem before heading to Cairo.
Officials from Hamas had suggested on Tuesday that a truce would come into effect at midnight, but Israel later said it had not agreed to a text.
Israel's demands include no hostile fire of any kind from Gaza and international efforts to prevent Hamas from re-arming, while Hamas is demanding an end to the blockade on Gaza and targeted killings by Israel.
Israel launched its current offensive a week ago with the killing of Hamas military leader Ahmed Jabari. The Israeli government says his assassination, and the subsequent offensive, is designed to end rocket fire from Gaza.
Israel has troops massed along the Gaza border but says it is holding off on a possible ground invasion as talks continue.
Twenty-eight people have been injured in a "terrorist attack" on a bus in Israel's commercial capital Tel Aviv, Israeli officials say.