The 33-year-old signed for the Owls last summer, but he was only handed 13 appearances in the Championship last term and is yet to turn out for them this season.
Speaking about the signing, Brentford manager Uwe Rosler admitted that he is pleased to have added more competition to his defensive ranks.
"Ever since Liam Moore left us last season [to go back to parent club Leicester City] we have been after a centre-half," he told the club's official website. "We worked on a few things in the transfer window and we got Ben Nugent in from Cardiff City on loan but I felt we needed more competition in that department.
"With Jake Bidwell out injured and Scott Barron coming back from a long layoff and then picking up a groin problem that meant he couldn't play against Bradford City on Saturday we needed to bolster the defence. Martin had a bunch of experience. He is a big unit."
Taylor started his career with Blackburn Rovers, before having spells with Birmingham City and Watford.