The attacker suffered the injury in Sunday's 4-0 La Liga win over Real Sociedad and was withdrawn from the game four minutes before the break, having opened the scoring at the Vicente Calderon.
The club confirmed on Monday that the former Barcelona forward sustained damage to his left hamstring.
"David Villa suffered an elongation/strain without rupture (grade I) of the bicep femoris muscle on the back of the left thigh," the club stated on their official Twitter account.
Atletico have not set a timescale on Villa's return to action, although he will likely miss Wednesday's Copa del Rey semi-final first leg clash with Madrid, with reports in the Spanish media suggesting he could be sidelined for up to 10 days.
Villa has 13 goals in all competitions since moving from the Spanish champions in July.