The suspension applies to a future playoff game, should Stony Brook qualify for the postseason.
Faiella, a junior linebacker/fullback who played in 13 games last season, will be allowed to play during the regular season.
Faiella's tweet was sent during the FCS playoffs and was directed at Towson University student-athletes.
"This was a very unfortunate incident, but racially insensitive characterizations are not acceptable and will not be tolerated," Division I Football Championship chairman Jim O'Day said in a statement. "The offensive language of this nature by Mr. Faiella, whether intentional or not, was unsportsmanlike and discredited the championship overall."
Stony Brook athletic director Jim Fiore said that when the university was informed of the post, it directed Faiella to remove it immediately.
"We're using it as a learning opportunity," Fiore said. "He's met with the appropriate people on campus, he's very remorseful."
Faiella, who is from Freehold, N.J., was not available for comment. His mother, Theresa Faiella, said she had not been in touch with her son to discuss the NCAA announcement and would have no comment.
Fiore said he apologized to Towson athletic director Mike Waddell, who was unavailable for comment Wednesday. Michael R. Harris, Towson's senior associate director of athletics, said, "Since this decision did not directly involve Towson, we do not have a comment."
Stony Brook appealed the ruling, saying Faiella should be suspended from the first game of the 2012 regular season -- and not the playoffs -- so the penalty could be served more swiftly. The NCAA denied the appeal, saying the suspension must be served during the playoffs. The university accepted the result. "We're moving on," Fiore said.
A spokesman for the Big South Conference, to which Stony Brook belongs, said it planned no action