Ted Lieu, the member of the House of Representatives from California’s 33rd district, called the President “paranoid like Nixon”.
The Democrat also suggested that he was “in trouble” and that danger was posed by Mr Trump.
“Mr President: If there was a wiretap at Trump Tower, that means a fed judge found probable cause of crime which means you are in deep s***,” Mr Lieu tweeted.
“Either @realDonaldTrump is paranoid like Nixon, or judge found probable cause of crime for #wiretap. Either way our President is in trouble,” he said in a further tweet.
Mr Trump also made the allegation against his predecessor on Twitter and did not provide any evidence to support his claim.
"Terrible!" the President wrote. "Just found out that Obama had my 'wires tapped' in Trump Tower just before the victory. Nothing found. This is McCarthyism!"
Soon after he added: "Is it legal for a sitting President to be "wire tapping" a race for president prior to an election? Turned down by court earlier. A new low!
"I'd bet a good lawyer could make a great case out of the fact that President Obama was tapping my phones in October, just prior to election!”
Mr Trump also described Mr Obama as a “bad (or sick) guy”.
“How low has President Obama gone to tapp [sic] my phones during the very sacred election process. This is Nixon/Watergate. Bad (or sick) guy!"
Mr Obama's spokesman denied the allegations and added that a “cardinal rule” of the Obama administration was that no White House official ever interfered in any Justice Department investigations.
“As part of that practice, neither Obama nor White House official ever ordered surveillance on any US citizen. Any suggestion otherwise is false,” Kevin Lewis said.