One of several Facebook groups calling for the 39-year-old to be freed has attracted nearly 30,000 members.
Other pages have also been joined by thousands of supporters, some of whom have suggested raising money for Sgt Blackman's family.
Sgt Blackman was convicted at a recent court martial of murdering a severely injured Taliban fighter.
Sentencing the ex-serviceman, a judge told him: "You treated that Afghan man with contempt and murdered him in cold blood."
Sgt Blackman was also "dismissed with disgrace" from the Royal Marines over the killing, which took place in Helmand province in 2011.