Bankruptcy Judge Kevin Gross ruled the team can accept bids to air games starting in 2014. The team would receive bids by Jan. 13 and complete sale by April 30.
"I just think it's in the debtors' best interests," said Gross, who told attorneys he would issue a formal written ruling in a few days.
The move is a key component of the Dodgers strategy to emerge from bankruptcy.
Fox Sports complained about the proposed sale process, saying it violated certain protections that Fox had under its current contract including an exclusive 45-day period starting in October 2012 to negotiate a contract extension with the Dodgers.
However, Gross overruled the objection. The Dodgers argued that because of discussions with Fox during the bankruptcy, the 45-day negotiating period actually began Nov. 30, giving Fox less than six weeks to renegotiate.
Fox Sports attorney Greg Werkheiser plans to file an appeal.
"While we are disappointed in the judge's decision, we understand the court process and will appeal this decision to protect our contractual rights," Fox said in a statement. "Those rights are material and valuable, and the current owner accepted them as binding when he purchased the team in 2004."
Gross did not immediately grant the request but noted that he always includes a "courtesy stay" in his rulings. He did not offer any other details.
Dodgers attorney Bruce Bennett also seemed disinclined to go along with the request.
"We're talking about burning up a couple of days," said Bennett, who told Gross he would talk to Fox attorneys and let the judge know by Friday whether the two sides can agree on how much time is left for the negotiations.
Sports media expert Edwin Desser, who testified on Fox's behalf, said he expects Time Warner to be the No. 1 bidder once the game rights are up for sale. He also said Fox could be put at a disadvantage by allowing bidders to see the details of Fox's discussion with the Dodgers during the exclusive negotiation period.
Fox attorneys have also questioned the April 30 deadline, which happens to be the deadline for former team owner Frank McCourt to pay his ex-wife, Jamie, $131 million as part of their divorce settlement.
The Associated Press contributed to this report.