Mavhaire was also stripped of his Zanu-PF Politburo post after it was discovered he was working with a cabal led by expelled former Vice President Dr Joice Mujuru that was angling to topple President Mugabe.
He wants the maintenance fee reduced to $200 on the basis that his financial position has substantially changed.
The maintenance hearing has been set for January 18 next year.
Mavhaire argued that the $300 maintenance fee he is paying was determined by his salary and his position as a Cabinet minister.
“I am no longer a Cabinet minister,” he said in his application.
“I have also been relieved of my senatorial position and I have not had a guaranteed income since January 2015.”
Mavhaire said the mother of the child, Makosi Mildred Bere, was aware of the changes of his financial position and had agreed to the relief sought.
“By agreement with her since April 2015, I have been paying her maintenance for the child at the rate of $200 monthly,” he said.
Mavhaire said his lawyers Mutumbwa, Mugabe and Partners advised him that the verbal agreement between him and Bere ought to be made an order of the court, hence the application.
He said his application was necessitated by the fact that some of the payments were made in arrears, a clear indication of the financial hardships he is facing.