The 21-year-old, who joined the Owls from Rangers in July 2012, has made the temporary switch to Fratton Park after making only nine appearances for Wednesday this season.
He has not featured for the Sky Bet Championship club since he was substituted at half-time in the 2-0 victory at Reading on February 8.
Pompey boss Richie Barker told his club's official website: "We were eager to bring Rhys in when we knew he was available because he's a quality player who will help keep possession in the centre of the park.
"He hasn't been in the Sheffield Wednesday side recently and is hungry to play. He jumped at the chance to come here, which is a good sign."
Portsmouth have also extended Brentford midfielder Toumani Diagouraga's loan stay on the south coast until the end of the campaign.
Diagouraga has made six Sky Bet League Two appearances since his initial move from the Bees last month.
Barker added: "Toumani has got better and better with every game and I think he'll have a big impact in our remaining matches this season."