Eric Bolling, a long-time host at the network, allegedly sent the messages on separate occasions several years ago.
His lawyer described the claims as "untrue and terribly unfair". Fox News said an investigation was under way.
It is the third high-profile harassment case to hit the conservative cable news outlet recently.
Citing 14 unnamed sources, the Huffington Post, a politically liberal news site, reports that Mr Bolling sent unsolicited photos of male genitalia by text message to at least two colleagues at Fox Business and one at Fox News.
"Eric Bolling has been suspended pending the results of an investigation, which is currently underway," a Fox News spokesperson said.
Mr Bolling's lawyer, Michael Bowe, told Reuters news agency: "The anonymous, uncorroborated claims are untrue and terribly unfair.
"We intend to fully cooperate with the investigation so that it can be concluded and Eric can return to work as quickly as possible."
Other allegations of sexual harassment involving top Fox News stars recently included:
Bill O'Reilly, who was dropped from the channel in April following reports that five women had received $13m (£10m) in payouts because of his behaviour. He denied the allegations
Roger Ailes, who resigned as chairman of Fox News following several accusations of harassment by female employees, which he denied. He died in May