Hannah, 33, has scored one goal since joining the Owls in February from BetVictor Northern Premier side Gainsborough Trinity.
I'm delighted to extend my stay to the end of the season," said Hannah.
"I've enjoyed my first month with the club. Great club moving in the right direction.
"Let's finish the season strong and get the job done."
The club have also confirmed that Rieves Boocock has returned to parent side Doncaster Rovers, following the expiry of his short-term loan.
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