Trippier, capped 46 times, picked up the problem during Newcastle's 3-0 home win over Wolverhampton Wanderers last weekend.
Newcastle visit 11th-placed Chelsea in the Premier League on Monday, followed by an FA Cup quarter-final trip to Manchester City on March 16. England, meanwhile, host Brazil and Belgium at Wembley on March 23th and 26th, respectively.
"Kieran's injury is not too bad, a minor injury," Howe told reporters. "The scans showed enough to probably keep him out for the next two games, and we hope he will be back for the first game after the international break, although that's not guaranteed.
"There is every chance he travels to both games; he is very keen to stay with the group despite the injury. It highlights his leadership qualities.
"As far as I know he will not be going away with England."
Howe backed Tino Livramento to step up in the absence of Trippier. Livramento moved to St James' Park from Championship side Southampton in August last year.
"It has been a brilliant start to his Newcastle career, Tino has handled himself well, played ever so well," he said.
"It goes without saying how good he is athletically and that showed with his goal against Wolves, showed his running ability and then his technical quality. I have been delighted with how he has started here."
Newcastle, eighth in the league with 40 points from 27 games, are looking to rediscover their best form having already exited the Champions League.
"We are running out of games and the season seems like it has gone so quickly, we are here now with minimal games left and we are trying to maximise on every game," Howe said.
"We have a bit of form behind us and we are still trying to recapture our best performance levels.
"We have high expectations of ourselves and we are not where we want to be, but hopefully we can get back to 100% as quickly as possible."
