The Brexit negotiations with the EU were due to start on 19 June but Moody's said the fact that the Conservatives had lost their majority would delay the start of the talks.
It will "complicate and probably delay Brexit negotiations", it warned.
Moody's said the election result could put pressure on the public finances.
The "inconclusive" outcome of the general election may mean the government placed less priority on cutting the budget deficit, the agency said.
This would be negative for the UK's credit rating and make it more expensive for the country to borrow money.
As a result, Moody's said it expected fiscal risks to increase because in its view the budget deficit will increase both this year and next.
"The election outcome, with significant gains for the Labour Party, which had campaigned for increased public spending, will likely be seen as a 'vote against austerity', it added.
"The public debt ratio will rise further and for longer than we had expected, placing the UK among the few highly rated European sovereigns whose public debt is still rising."
However, Moody's said the election result suggested an "electoral shift" away from the "hard Brexit" that Prime Minister Theresa May had ostensibly sought.
As a result, Moody's said the government may now consider "softer" Brexit options, which would be positive for the country's credit rating.
Earlier, Brexit Secretary David Davis told Sky News that negotiations on leaving the EU would begin next week. but not necessarily on 19 June.
"My permanent secretary is actually in Brussels today talking to them about the details," he said.
"It may not be on the Monday because we also have got the Queen's Speech that week and I will have to speak in that, and so on."
Meanwhile, S&P Global Ratings released a note saying the outcome of the snap election and the hung parliament should have no immediate impact on the UK's rating.
"Our ratings on the UK already take into account a less predictable policy framework following the vote to leave the EU in June 2016," it said.
It also said it believed the lack of an overall majority for any one part was likely to delay Brexit negotiations. "We do not exclude the possibility of another snap election."
Separately, S&P economist Jean-Michel Six said: "In terms of the [UK's] outlook for growth, it's clear that things are not going in the right direction."
"This latest bit of instability can only weaken the business environment and consumer confidence," he said.
S&P said the UK's outlook remained negative.
Moody's rates the UK as Aa1 negative - one notch above the other two big agencies, S&P and Fitch.
The UK general election result could delay Brexit talks and be negative for the economy, credit ratings agencies Moody's and S&P have warned.