The procedure will be performed by Dr. Brian Schofield, a hand specialist.
The injury is believed to have occurred more than a week ago when Markakis slid into a base. He then aggravated it during his final at-bat Tuesday against the Toronto Blue Jays.
The Baltimore Sun reported Thursday that Markakis is expected to miss 2-4 weeks.
The Orioles had feared worse.
"If you had told me that was what it was going to be, I would have signed up for it in blood," manager Buck Showalter told MLB.com on Thursday. "It's not that bad."
This will be the first trip to the disabled list for the 28-year-old Markakis, one of Baltimore's most durable players. He played in at least 160 games in each of the previous three seasons and never has participated in fewer than 147 in a single season since coming into the league in 2006.
Information from The Associated Press was used in this report.