The Madrid captain was substituted in the 78th minute in Shkoder after taking a tumble in the penalty area as Koke took a corner and is likely to face a lengthy spell away from action.
Ramos was attended to by the Spanish team doctor Oscar Celada in Albania and was hastily taken off with reports suggesting it could be a month before he plays for either club or country again.
"Sergio's injury looks like a strain and we hope that's all it is but the doctors are the ones who have to determine what it is. He's a very important player for us and his club," the Spain coach, Julen Lopetegui, told a news conference.
Ramos will undergo further tests when he returns to the Spanish capital on Monday to determine the extent of his injury.
Although Ramos has endured a stumbling start to the season, conceding four penalties for club and country, his absence will be keenly felt by Real and coach Zinedine Zidane, who has recently been without Brazilian duo Marcelo and Casemiro and midfield maestro Luka Modric.
The former Real great has also faced serious criticism for the team's stuttering run of four consecutive draws in all competitions, which culminated in a shock 1-1 draw at home to Eibar last Sunday.
Ramos is likely to miss Real's La Liga games against Real Betis, Athletic Bilbao, Alaves and Leganes and two Champions League group games with Legia Warsaw.
He is also doubtful for Spain's World Cup qualifier with Macedonia on 12 November and friendly versus England on 15 November.
Additional reporting by Reuters.Reuse content