On their official website, the Gunners said he "will undergo further specialist assessments" this week to determine the extent of the problem.
Kolasinac started the match but had to be taken off after just 18 minutes.
The Bosnia and Herzegovina international, who missed three games in December with an ankle injury, suffered the injury when he landed heavily after a coming together with Everton's Djibril Sidibe.
Simon Collings of the Evening Standard reported he could be out for over a month:
Fortunately for the Gunners, Bukayo Saka has shone at left-back this season despite being a winger.
The 18-year-old assisted Arsenal's first goal against the Toffees with an excellent cross:
He has been an enormous source of creativity for the Gunners this season:
While Kolasinac's injury is not ideal for Arsenal, it will at least allow Saka to continue gaining invaluable first-team experience in his absence.
What's more, Kieran Tierney is also returning at the right time after he dislocated his shoulder in December.
Per the Gunners' website, he is targeting a return to full training by the end of February.