Essien found the top corner at Stamford Bridge to help Chelsea set an English record of 64 unbeaten home matches in the league with a 3-2 win, but the midfielder was then substituted with 21 minutes remaining.
"It was something in the knee ligament," said Mourinho.
"He was in pain, I had two midfielders on the bench so I made the change immediately.
"If you asked me, I don't know if he'd be fit for Wednesday against Reading."
The positive news for Mourinho was Didier Drogba coming off the bench after missing the Community Shield through injury, while Joe Cole was an unused substitute.
Claude Makelele and Paulo Ferreira are expected to train on Monday but Andriy Shevchenko is not ready to return yet following a reported back complaint.
Extending their home record will wait until later in the month as Chelsea travel to Reading on Wednesday and Liverpool next weekend.
Mourinho's personal record is even more remarkable and he will reach a century of unbeaten league matches at home if Chelsea avoid defeat against Portsmouth next time out at Stamford Bridge.
"I'm on 99 and I hope my friend Harry Redknapp doesn't kill my record in the next game at home because I would love to reach 100," said the Portuguese boss.
Defeating Birmingham, however, was not straightforward after the visitors took an early lead through former Chelsea striker Mikael Forssell.
Claudio Pizarro and Florent Malouda marked their home debuts with goals but Olivier Kapo levelled matters before the break with a stunning strike.
Essien found the top corner five minutes into the second half and the attacking continued from both teams.
"It would be better to score five or six goals and win in a different way but the game was great, not just because Chelsea played great attacking football but because Birmingham also were great," added Mourinho.
"Teams from the Championship, especially in the first period after promotion, come with a winning spirit because that is what got them promoted.
"They could have scored three and we could have scored six or seven."