Members began posting comments on the microblogging site with the hashtag #nowthatchersdead soon after the news was announced.
But it was apparently misinterpreted and led to a flurry of Tweets suggesting it had upset the pop star's fans.
Comedian Ricky Gervais attempted to set the record straight, writing: "Some people are in a frenzy over the hashtag #nowthatchersdead.
"It's 'Now Thatcher's dead'.
"Not, 'Now that Cher's dead'".
Other Twitter users sought to reassure followers. One wrote: "It's OK people, @cher is still very much alive".
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