The White House last week warned Samsung against using the president's likeness for commercial gain, after Ortiz used one of its cell phones to snap a picture of himself and the US president.
The picture showed a beaming Obama alongside Ortiz, holding a Red Sox jersey presented by the team.
To the displeasure of the White House, Samsung retweeted the shot taken of the baseball slugger and the president, which went viral on the Internet.
The White House which made its objections public a couple of days after Samsung's marketing stunt on Sunday said its attorneys were pursuing the matter.
"We've had conversations with Samsung about this and expressed our concerns. We've left that conversation between the lawyers," White House Senior Adviser Dan Pfeiffer told CBS television's Face the Nation program on Sunday.
Obama "obviously didn't know anything about Samsung's connection to this. And perhaps maybe this will be the end of all selfies," said Pfeiffer.
"But in general, whenever someone tries to use the president's likeness to promote a product, that's a problem with the White House."
Ortiz and his fellow Boston Red Sox teammates had been visiting the White House on a belated victory lap, after winning the World Series baseball championship last year.
SportsBusiness Journal later reported that Ortiz, winner of the most valuable player award in last year's World Series, has a freshly inked endorsement deal with Samsung.
Presidential spokesman Jay Carney last week told reporters that "as a rule, the White House objects to attempts to use the president's likeness for commercial purposes."
Samsung caused a similar stir at this year's Oscars when host Ellen DeGeneres used one of its phones for a group selfie with a posse of smiling Hollywood A-listers.