"We are devastated to pass on the news we only just heard ourselves earlier tonight", said the heavy metal band's official Facebook page.
In a Facebook post, later members of the group said Clarke died in hospital where he was being treated for pneumonia.
The last surviving member of Motorhead's classic 1970s line-up, Fast Eddie Clarke, has died while being treated in hospital for pneumonia. Clarke was the last surviving member of Motorhead's so-called classic lineup, which included frontman Lemmy Kilmister and drummer Phil "Philthy Animal" Taylor, who died a month apart from each other in 2015.
Swedish musician Mikkey Dee, the drummer from rock band The Scorpions, and a member of Motörhead from 1992 to 2015, said: "This is awful news, the last of the three amigos".
"Fast Eddie... keep roaring, rocking' and rollin' up there as goddamit man, your Motorfamily would expect nothing less!" So this is a complete shock.
"I was looking forward to seeing him in the United Kingdom this summer when we [are] around with the Scorps..."
"Such a shock, he will be remembered for his iconic riffs and was a true rock and roller", he said. Now Lem and Philthy can jam with Eddie again, and if you listen carefully I'm sure you'll hear them, so watch out! "He took that style in a more metallic direction with Fastway, a more commercial hard-rock band he formed with former UFO bassist Pete Way".
"My thoughts go out to Eddie's family and close ones". He also released a number of solo albums. Motorhead is perhaps best known for its 1980 song, "Ace of Spades", which was featured on the popular video game Guitar Hero.