Speaking at a think tank, the levelling up secretary said the idea could help restore an "ethic of responsibility".
Mr Gove - who first proposed the idea in 2014 - said it would help tackle anti-social behaviour.
Downing Street said parents could already be fined for children missing school.
The idea of cutting benefits for parents of truants was first suggested by Labour Prime Minister Tony Blair in 2002, but it was dropped in favour of the current fines system.
Michael Gove resurrected the idea when he was education secretary under Prime Minister David Cameron but it was never implemented.
Speaking at an event held by Onward, a centre-right think tank, Mr Gove said: "Particularly after Covid, we need to get back to an absolute rigorous focus on school attendance.
"One idea that we considered in the coalition years - but which the Liberal Democrats blocked - I think needs to be reconsidered again, is linking parental responsibility for attendance and good behaviour to the state.
"One of the ideas that we floated in the coalition years - which as I say, the Liberal Democrats rejected - was the idea that if children were persistently absent, that child benefit should be stopped.
"I think what we do need to do is think radically about restoring an ethic of responsibility," he added.
Currently, parents whose children miss school in England can be issued with £60 fines, which rise to £120 if they are not paid within 21 days. They are normally issued by local councils.
They can also be ordered to attend parenting classes, or have a supervisor appointed to help them get their child into the classroom.
The use of fines dropped off during the pandemic due to an increase in home learning, but BBC research last year suggested they had started to pick up again.
Last year, the government set out plans to introduce new national guidelines in England on the issuing of fines, and make schools draw up their own attendance policies.
The measures were later incorporated into the Schools Bill - however this legislation was dropped in December after it hit hurdles in Parliament.
The NAHT, a union representing school leaders, condemned Mr Gove's suggestion, adding that it was "likely to be counter-productive".
"It is very hard to see how consigning children to poverty and starvation will improve their school attendance," general secretary Paul Whiteman added.
"Persistent absence can only be successfully tackled by offering help, not punishment."
Liberal Democrat education spokesperson Munira Wilson said: "If Michael Gove thinks that the solution to encourage children back to school is to impoverish them, then he is living in a different century".
The prime minister's official spokesperson said there were no plans to change the existing system.