Standard Sport understands that Morata has told close friends that he expects to be sidelined for a few days before resuming training next week.
Morata aggravated the problem during the first half of Chelsea’s 1-0 defeat to Manchester City on Saturday and asked to be substituted.
The 24-year-old was seen limping three days earlier following the victory at Atletico Madrid, but coach Antonio Conte admitted he had to “risk” playing the forward against Pep Guardiola’s side.
Spain confirmed late last on Sunday that the injury was serious enough to rule out Chelsea’s top scorer from their World Cup qualifiers against Albania and Israel on October 6 and October 9 respectively.
But should the former Juventus star return to training next week as expected, it will give him plenty of time to prepare for the trip to Selhurst Park.
Morata has made an impressive start to his career at Stamford Bridge having joined from Real Madrid for a club record £58m in July.
He has scored seven goals in just eight appearances and his early departure on Saturday was seen as a major reason why Chelsea struggled to cause a threat against Manchester City.
Conte made only two changes from the side that had played in Madrid less than 72 hours earlier and one of those was enforced as David Luiz was suspended.
The other was right wing back Victor Moses, but Conte revealed that resting Morata was not an option he could afford to consider.
He said: “You have to try not to put your players in difficulty, but also take a risk (of not playing them).
“It’s not simple for our wing backs. Moses is an important player for us and played two games against Stoke and Atletico.
“To play him three games in seven days you take a risk. With Morata it was the same, but I make this decision to risk Morata in this game because imagine (the reaction) if I decide to put Morata on the bench?
“You know that Manchester City is a really good team and you have to put the best formation in this type of game. In this type of game it is difficult to think about rotating the players.
“When there are these massive games you have to make the best decision and try to put the best players in.
“Honestly we can’t have regrets. We gave everything and all my players put in 120 per cent to get a good result.
“Sometimes you have to accept a bad result. The most important thing is to see fantastic commitment and attitude of my players – they gave everything.”
Chelsea have the same amount of points as they had at the same stage last season but captain Gary Cahill admits it will be tough to retain their title.
Manchester City and Manchester United are both unbeaten and sit six points clear of Conte’s side.
Cahill said: “They’re both getting very good results and scoring a lot of goals, but let’s see. We’re in September, so let’s get to Christmas, January time – hopefully we’ll be in and around the top and then we’ll see from there.
“We’re experienced, but it’s disappointing to lose points against Manchester City.
“We proved last season we’ve got enough to win the League, but we realise it’s very difficult.
“We’ve done it twice since I’ve been here and both times it’s been extremely difficult. Look at the strength of the teams around us, but it’s just important that we fight to the end.”