Landowners carry out culls from August that they say are necessary to protect grouse from disease so they can be shot for sport.
Campaign group OneKind said death rates of mountain hares are not monitored but it believes around 40% of those killed are shot for sport and 50% as part of organised culls.
The Scottish Government said numbers need to be controlled in some circumstances but it “will not tolerate large-scale culls of mountain hares”.
An independent review looking at the sustainability of grouse moor management, including mountain hare culling, is being established.
OneKind director Harry Huyton said: “Mountain hares are an iconic species in Scotland that should be protected.
“Our report shows that instead they are persecuted in enormous numbers for entertainment. This killing is unregulated, and there are no guarantees that it is not further driving the decline of these species or causing unacceptable suffering.
“Today, the day before the open season begins, OneKind is calling on the Scottish Government to take urgent action and introduce a moratorium on large-scale hunts and culls before the season gets into full swing.”
A Scottish Government spokesman said: “We have been very clear that we will not tolerate large-scale culls of mountain hares, but we recognise that numbers need to be controlled in some specific circumstances.
“Environment Secretary Roseanna Cunningham has already announced the Scottish Government is setting up an independently-led group to examine the sustainability of grouse moor management, which includes mountain hare culling.
“We are also commissioning research into the costs and benefits of large shooting estates to our biodiversity and economy.”