Franco, a shortstop, has not played since being placed on leave last week, ruling him out of the Rays' road series against the San Francisco Giants.
On Tuesday, MLB said Franco's leave had been extended indefinitely after an agreement between the league and the Major League Baseball Players Association (MLBPA).
"Per an agreement between MLB and the MLBPA, Wander Franco has been placed on Administrative Leave until further notice as MLB continues its ongoing investigation," MLB said in a statement.
"We will comment further at the appropriate time."
The league said Franco's leave period was "not punitive," and the player would continue to be paid by his club.
The Rays voiced support for the league's decision.
"The Tampa Bay Rays are dedicated to upholding high standards of integrity both on and off the field," the team said.
"We appreciate the understanding and patience of our fans and supporters as this process unfolds. We will have no further statements on this matter until MLB completes its process."
Franco has been one of the best players in baseball this season, blasting 17 home runs with 58 RBIs and 124 hits from 442 at bats.
