After an X-ray on Sunday, Headley visited a hand specialist in San Diego on Monday.
"You hate to see it happen," Padres manager Bud Black said. "It's unfortunate for Chase and the Padres."
The Padres open the regular season on April 1 against the Mets at Citi Field.
After a first-inning single, Headley jammed his thumb against the second-base bag when he slid trying to break up a double play on Sunday. He played defense in the bottom of the inning before leaving the game.
"He went to slide into second base and got stuck and twisted around, and his thumb ended up hitting the bag ... his thumb was in a bad spot," Black said.
Headley led the NL in RBIs (115) in 2012 and had a breakout year at the plate, hitting a career-high 31 home runs. A switch-hitter, Headley produced big numbers both in pitcher-friendly Petco Park and on the road. He also finished fifth in the NL MVP Award voting.
Headley has hit .448 in 29 at-bats this spring while essentially playing every other day. Black has eased his regular position players into the lineup due to the longer Spring Training.
The Padres have two in-house options they could use at third base: Logan Forsythe and Jedd Gyorko.
"There's a lot of options," Black said.
But Forsythe, considered a plus defender at third base, hasn't played since March 7 because of plantar fasciitis in his right foot. Forsythe said Monday that he hopes to return to games by Tuesday.
Gyorko, who mostly played third base in the Minor Leagues, has exclusively been playing second base this spring and is considered the favorite to start there on Opening Day.
On Friday, Headley was contacted by Team USA to gauge his interest in playing in the World Baseball Classic if the team advanced to the semifinals in San Francisco. He agreed to do so, but Team USA was eliminated later in the day by Puerto Rico.
As for his injury, this isn't the first sliding mishap Headley has endured. He missed 39 games in 2011 due to a fractured finger on his left hand he suffered when it hooked the second-base bag in a game at Pittsburgh.
Missing Headley, who was the NL Player of the Month in both August and September in 2012, for any length of time could impede an offense that amassed the fifth-most runs in the league over the final 86 games of last season.
Headley set a franchise record last season by reaching base safely in 146 games, eclipsing the previous mark of 144 set by Hall of Fame outfielder Tony Gwynn in 1987.
Now the Padres are faced with opening the regular season without their top offensive threat.
"It's tough, that wasn't the plan," catcher Nick Hundley said. "But we've got guys in this locker room who can and will step up. You're not going to have one guy replace Chase. You have to do it as a lineup."