Suleiman played for Al Whatba of Homs and was caught in an explosion just outide the team's hotel as they were about to head to training at the Tishrin stadium.
The 19-year-old died from his injuries in hospital and the Fifa president, like many others, has expressed his sorrow at what is a truly tragic event.
"I was very shocked and saddened to learn of the tragic incident on Wednesday that claimed the life of a Syrian football player and left four other people wounded," Blatter wrote, in an open letter to the nation's Football Association president Salah Edeen Ramadan.
"Both personally, and on behalf of Fifa and the worldwide football community, I wish to extend our deepest condolences to the family and friends of the young footballer, to you and to everyone at the Syrian Football Association."
"The football community stands by their side at this time of sorrow. I hope that the other four wounded people are in a stable condition and wish them much strength and courage and a speedy recovery. My thoughts are also with them and their families."