Neither Turner nor the Nationals have given a timetable for his recovery or even announced the nature of the surgery (broken bone? ligament damage? etc.). Spring training opens in approximately three months, so Turner has some time to heal up and get ready to help Washington defend their title.
“Only took 7 months to get this finger fixed but now my ring will fit better!” Turner said in the caption.

It wasn’t until after the Nationals won the World Series that Turner revealed he was unable to bend his right index finger fully. Here he is talking about the finger injury and showing its limited movement during an MLB Network segment:
Defensively, Turner made six throwing errors in 1,065 1/3 defensive innings in 2019 after making five throwing errors in 2,279 1/3 innings at shortstop from 2015-18. It seems he had more trouble making throws with the injured finger than he did swinging a bat.  If the injury hampered Turner at the plate, it didn’t show during the regular season. He hit .296/.352/.487 with 17 homers in 118 games after returning from the injured list, and he stole 31 bases in 36 attempts as well, so he wasn’t shy about sliding into bases with the broken finger. Turner mostly struggled in the postseason, hitting .233/.291/.329 in 17 games.
Seventeen days after helping the Nationals win the World Series, Turner finally underwent surgery to repair his finger. He posted a post-op photo on Instagram on Saturday:
On April 6, four games into the season, Nationals shortstop Trea Turner broke his right index finger trying to lay down a bunt. The injury sent him to the injured list for six weeks, and, once he returned, he played despite not being able to fully bend the digit. That meant he was unable to grip a bat properly or even grip a baseball to throw it properly.