"The Reform Party needs a new leader. Farage doesn't have what it takes," Musk said on his social media platform X on Sunday, a few hours after Farage described him as a friend who made Reform look "cool".
Musk - a close ally of US President-elect Donald Trump - had seemingly backed Farage and posed for a photograph with him last month.
Reform won 4.1 million votes or 14 per cent of the total and five seats in parliament in last July's national election.
Media have speculated recently that Musk might make a big cash donation to Reform to help it challenge the dominant Labour and Conservative parties.
But Farage has distanced himself from comments made by Musk in support of British anti-immigration and anti-Muslim activist Stephen Yaxley-Lennon, known by the pseudonym Tommy Robinson, who is serving a prison sentence for contempt of court.
Farage responded to Musk's post on Sunday saying: "Well, this is a surprise! Elon is a remarkable individual but on this I am afraid I disagree. My view remains that Tommy Robinson is not right for Reform and I never sell out my principles."
Last month, Musk endorsed the Alternative for Germany, an anti-immigration, anti-Islamic party labelled as right-wing-extremist by German security services ahead of national elections in February.
Musk has previously sought to influence British politics and has repeatedly criticised Prime Minister Keir Starmer.
Last week the Tesla founder called for a national inquiry into the handling of cases of rape by men of Pakistani heritage of underage girls at a time when Starmer headed the government's prosecution service.
A 2014 inquiry found at least 1400 children were subjected to sexual exploitation in Rotherham, northern England, between 1997 and 2013.
On Sunday, UK health minister Wes Streeting defended Starmer and another member of his cabinet, Jess Phillips, who incurred Musk's ire for reportedly saying that any fresh inquiry should be handled by the local authority.
"It's all very easy to sit there and fire off something in haste and click 'send' when people like Keir Starmer and Jess Phillips have done the hard yards of actually locking up wife beaters, rapists and paedophiles," Streeting told the BBC.
