Mr Mutai was seen being carried piggyback-style by a younger man over streaming water while leading a central government damage assessment team.
He apologised at the time but on Wednesday joked at a fundraiser with supporters that the "(rubber) boot industry made money" - implying that sales rose as people saw the need for such footwear.
On Friday, Yoshihide Suga, the government's top spokesperson, said it accepted Mr Mutai's resignation, which had been proffered the day before, over the blunder.
"We thought it was extremely regrettable as his comments were inappropriate, raising questions over whether he sincerely reflected on his behaviour last year," Mr Suga said.
In September, Mr Mutai, clad in a blue work uniform and black shoes, was apparently trying to avoid getting his feet wet. Most other accompanying officials wore long rubber boots for protection.
"I'll be in trouble if this is caught on camera," Mr Mutai was seen saying on after being put down.
Despite stepping down as a vice minister, Mr Mutai remains a member of parliament.