The letter, which purportedly bore Mr Solanki's signature, is addressed to Congress president Sonia Gandhi.
Mr Solanki is resigning from the post of state president being aggrieved by certain decisions taken by the party, including distribution of tickets, the letter says.
He is aggrieved because tickets were sold to undeserving candidates, the letter has Mr Solanki saying.
"The letter is fake and is a mischief played on the Congress party. We will register a complaint before the Election Commission against this," Congress spokesperson Manish Doshi said.
Mr Solanki told PTI that his family is wedded to the Congress ideology for four generations, so the question of resigning does not arise.
"The writing on the wall is very clear as 22 years of BJP's misrule has disappointed all sections of the society as wrong claims of development have failed to convince the people of Gujarat," he said.
Mr Solanki also took to Twitter to clarify that the letter was fake, and blamed the ruling BJP for "spreading lies on social media".
"BJP is nervous and rattled by the surging popularity of Congress and as people of all sections are coming together to root out anti-people govt, out of sheer desperation they are spreading such lies on social media to deflect from the real issues," he tweeted.