In a statement issued on Friday, the club announced it would cease trading 'until further notice' due to the pressures of the Covid-19 pandemic.
It is believed Mission's adjacent sister club, Tunnel Leeds, will also close its doors.
The manager, who wished to remain anonymous, told the Yorkshire Evening Post that Leeds had lost 'such a massive part' of the nightlife in the city due to the closure.
He said staff were informed of the closures on Friday and it was 'devastating news'.
It is believed that around 30 staff members will be affected by the closure.
A fundraiser has now been launched to 'save the club' on GoFundMe.
A post on the fundraiser - set up by a loyal customer and supported by the staff - read: "Mission and Tunnel are part of the LGBTQQIAAP+ history in Leeds; acting a safe space and a place to celebrate queer culture for locals and students. Coronavirus has hit a lot of businesses hard, but the nightclub industry has been crippled more than most.
"Multiple staff and performers face unemployment and a special piece of Leeds will be lost forever .
"If you’ve ever spent a night there you’ll get it, if you haven’t you need to. Save our club!"
More than £400 has been raised in the first few hours of fundraising.
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