Frank Lampard reveals star's 'unfortunate' injury and big Everton misses for Leeds United visit
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Mina will sit out for two months or so through a quad injury, joining fellow centre-half Ben Godfrey, who has torn his hamstring, on the sidelines.
At the other end of the pitch Lampard also has issues, with Demari Gray and ex Leeds man Fabian Delph also out.
"Yerry Mina is an unfortunate injury, probably between eight to 10 weeks," said Lampard.
"It's a strong injury around his quad, it's disappointing for us all. I've realised in the first few weeks he's a big leader, a big personality, a positive man and he's a good player for us.
"I was aware on the night, our medical team were wary of the type of injury from Yerry's description of what he felt and our worst fears were confirmed a day or so later. We have to be positive around him and move on in the short term until he comes back.
"Demari won't be fit for Leeds, hopefully [it's just] a minor knock around his hip and Fabian isn't ready yet, he's a few weeks away."
Vitalii Mykolenko and Abdoulaye Doucoure are also among Lampard's absentees but the recently-appointed manager insists he has confidence in the available players.
"Two big injuries for us, centre-back, international players like Ben and Yerry," he said.
"We have players stepping up there. The options are becoming tight, they're big misses for us. I have confidence in the squad and we'll just have to dig in.
"Doucure is still out, he's one of the best midfielders in the league of his type. I have belief in the squad though and sometimes digging in is the only way. We're missing big players, which would obviously damage any squad."
Lampard does have Dominic Calvert-Lewin available as he continues to try and get his season back on track after a toe injury, but the Toffees manager wouldn't confirm if the England striker will start against the Whites.
"Dominic is in the squad for tomorrow," he said.
"That's for us to decide [if he starts], he's been working all week with us so we'll decide that tomorrow."