The NHL's top-scoring defenceman left Wednesday's 3-1 win over the New Jersey Devils in the third period after he was hauled down by Devils forward Steve Bernier.
Giordano skated in pre-game warmups Friday as Calgary got set to play the New York Islanders, but he did not play.
"Gio is our captain and a warrior," Calgary head coach Bob Hartley told the Associated Press. "When Mark says he can't play, that says a lot. He really wanted to, but couldn't."
"We want to make sure we're being diligent in terms of the protocol on all of the medical side of things," general manager Brad Treliving told reporters prior to the game Friday on Long Island. "Once we know where Mark's at, definitively, we'll share that ... there's still some things (we) have to go through here."
Giordano has 11 goals and 37 assists in 61 games and is plus-13.
The Flames are trying to stay in the playoff mix as they continue a seven-game road trip. Calgary ranked ninth in the Western Conference, but tied in points with eighth-place Los Angeles, prior to Friday's 2-1 loss to New York.