Estevao was visibly upset when he left the field against Manchester United.
“He was devastated,” Chelsea head coach Liam Rosenior said after the match.
“He was crying at half-time. I’m really devastated for him.”
Brazil face Morocco in their opening World Cup group stage match on 13 June.
It is the second time this season Estevao has suffered a hamstring injury. Captain Reece James, forward Cole Palmer and young attacker Jamie Gittens are also currently sidelined with similar issues.
The Brazilian has scored eight goals and provided four assists in 36 appearances during his maiden season at Stamford Bridge.
He joined Chelsea in the summer from Brazilian club Palmeiras for an initial £29m fee, which could rise by a further £51m through add-ons.
Chelsea lost 3-0 at Brighton on Tuesday and have dropped to seventh in the Premier League table, with Champions League qualification now in doubt and Rosenior’s future increasingly uncertain.