A statement released by Anzhi said the 20-year-old was driving to his family home when his car was targeted by machine-gun fire. He subsequently died as a result of his injuries on the way to hospital.
The statement added that the police have yet to discover motive for the attack.
"Football club Anzhi conveys the sincerest condolences to all the dearest of Gasan," the statement added. "It's caused huge grief for all of us.
"Gasan would have celebrated his 21st birthday on January 17. [A] kind-hearted boy, Magomedov was true to himself on the field."
Magomedov represented Anzhi at youth and reserve-team level.
Anzhi's general director, Sergey Korablev, added: "We grieve together with everyone who was dear to Gasan.
"I hope the police quickly find the killers and they suffer just punishment."
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