The 27-year-old learned of the failed test earlier this week and said he had "let a lot of people down".
Ellesse said they "cannot condone the lifestyle choices he has made".
The Briton signed with Ellesse in March after buying his own kit at this year's Australian open because his Nike deal had run out at the end of 2016.
Evans, who has accepted the finding, could be banned for up to four years for an anti-doping violation, according to International Tennis Federation (ITF) rules.
Liam Broady, who plays fellow Brit Marcus Willis in the second round of Wimbledon qualifying on Wednesday said: "Evo's a mate. I know Dan can only blame himself but I think Dan can often portray that he doesn't care about a lot of things, he's quite a cool cookie.
"But no-one loves tennis more than Evo does and this will hurt him. I hope he's OK, to be honest. My only concern is about Dan. He's a friend."
Willis added: "It's a shame. He's a cracking tennis player and nobody really knows what happened. He had a moment where he was stupid and it's cost him a little bit.
"But I've no doubt he'll be back up there after his ban."
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Sportswear firm Ellesse have withdrawn their sponsorship of British number three Dan Evans after he tested positive for cocaine in April.