Hudson announced his retirement from professional baseball following the Dodgers' title-clinching victory in Game 5 of the World Series on Wednesday, Bill Plunkett of The Orange County Register reports.
Hudson allowed a pivotal grand slam to Anthony Volpe to earn the Game 4 loss against the Yankees.
Manager Dave Roberts said Wednesday that Hudson will be available for Game 3 of the NLCS against the Mets on Wednesday after dealing with a lower-body injury in Game 2, Bill Shaikin of the Los Angeles Times reports.
Hudson got the save in Tuesday's win over the Mariners, allowing a hit over a scoreless inning.
Hudson earned a hold against the Giants on Thursday, walking one batter and striking out two in a scoreless sixth inning.
Hudson did not walk or strike out a batter during a two-out save in Sunday's 9-6 win over the Red Sox.
Hudson wasn't available out of the bullpen for Sunday's 4-3 loss to the Tigers due to back stiffness, Fabian Ardaya of The Athletic reports.
Hudson earned a hold against Kansas City on Sunday, striking out two batters in a perfect eighth inning.
Hudson (2-1) gave up two hits and a walk while striking out one in a scoreless ninth inning during the first game of Tuesday's doubleheader against the Mets, recording the win in a 5-2 extra-inning victory.
Hudson is the likely favorite for save opportunities after Dodgers closer Evan Phillips (hamstring) was placed on the 15-day injured list Sunday.