Muller was leader for just 57 days but said the role has taken a "heavy toll on me personally, and on my family, and this has become untenable from a health perspective".
Bridges took over from Sir Bill English as leader in February 2018.
Prime Minister Jacinda Ardern has passed her best wishes on to Muller and his family.
"No matter what side of Parliament you're sitting, politics is a difficult place," she said.
In a statement, NZ First leader Winston Peters said there was a "heavy price of trying to lead the National Party today".
He said Muller was a good man who would bounce back.
"Leading a divided and incompetent caucus would have tested even the best leader. Todd never had a chance given the fault lines of ambition, personality, and ideology that run deep through the National Party caucus."
ACT Party leader David Seymour said he was surprised at the move.
"Todd Muller is a hell of a nice guy. Being a leader of a political party on the national stage is an extremely competitive and bruising role.
"You just have to look at the human side of politics and say 'he gave it a go, good on him' and respect his decision."
He said from ACT's point of view, National needed to pick a leader.
"I will have worked with five National leaders by the end of this week ... hopefully not six by the end of this election."
His role was to ensure ACT was a big party so as to have a chance at changing the Government, he said.
But Massey University professor and political commentator Claire Robinson said Muller was naive.
"I think it shows how completely unprepared he was for the role.
"He obviously thought he was God's gift to the National Party and taking over from Simon Bridges ... and I think he thought it was going to be so easy simply to role out a whole lot of new policies under his leadership and everybody would think: 'Oh good, everything is okay now'."
Many social commentators said Muller's health was visibly declining:
