Maynor, the 20th overall pick in this year's draft, was averaging 5.2 points and 3.1 assists in 26 games with the Jazz this season. He figures to take over as the backup point guard for Oklahoma City, which waived reserves Shaun Livingston and Mike Wilks to clear room for him on the roster.
Kevin Ollie and Kyle Weaver, the usual backups to starter Russell Westbrook, are both injured.
Oklahoma City also agreed to take on the $6.5 million contract of injured veteran Matt Harpring, who won't actually join the Thunder. Harpring, an 11-year veteran, hasn't played this season while recovering from an infection that developed after he had surgery on his ankle in the summer of 2008.
Harpring said earlier this month that he was giving up his comeback attempt, although he didn't say he was retiring.
The Jazz will get the rights to 2002 second-round draft pick Peter Fehse, who has never played in the NBA and is currently playing in the German League.
"Trading Eric was a difficult decision," Jazz general manager Kevin O'Connor said in a statement. "But, along with Matt's contract, it greatly helps reduce our luxury tax responsibility. Fortunately, with Deron [Williams] and a proven backup in Ronnie Price we feel that we have depth at that position."
Maynor made two starts earlier this season while Williams was away from the team, including a career-high 24-point outing against Cleveland.
The trade offers Maynor a reunion of sorts with Oklahoma's Jeff Capel, who recruited him to Virginia Commonwealth before leaving to become the Sooners' coach.
Livingston joined the Thunder late last season after recovering from a gruesome February 2007 injury in which he tore three ligaments in his left knee and dislocated his kneecap. He played in 10 games for Oklahoma City this season, including the past eight in a row after missing just under a month following surgery.
Wilks was signed after Livingston, Ollie and Weaver were all injured and played in four games.
"This was a difficult decision as we appreciate Shaun and Mike's contributions to this basketball team on and off the floor," Oklahoma City general manager Sam Presti said in a statement. "We wish them nothing but continued success."