The controversy arose after a self-styled watchdog group - the Network of Civilians to Protect the Nation, the Religion and the King - said monks were using the social networking site hi5 to flirt with women.
One user who called himself "Monk Chat" sent a message to a woman that said "(I) miss you," reported Thai Rath, Thailand's top-selling newspaper.
Buddhist monks must abstain from sexual behavior, which in practice means avoiding almost any contact with women. About 90 percent of Thailand's 65 million people are Buddhist.
Thai society expects most Buddhist males to spend at least two weeks in the monkhood during their lives to show their devotion to the religion. While most monks live by the religion's strict tenets, occasionally some flout the bans on sex or drinking.
Phone calls seeking comment to Bangkok's Mahachulalongkornrajavidyalaya University, the country's leading Buddhist training institute, were not answered Tuesday.
Charkapob urged other Thai Web users to look out for monks conducting themselves in an unseemly manner online.
"We urge people who use the site to tell monks to leave," Chakrapob said. "Other users need to show them that it is inappropriate for monks to chat with women online."
Last year, the Thai government blocked access to the YouTube video site for several months in a dispute about content deemed insulting to Thai King Bhumibol Adulyadej.
When asked about the possibility of blocking hi5, Chakrapob said the government needed to thoroughly consider its options because "the site is used as a database for many people and can be useful for many purposes."
The operators of California-based hi5 claim it is the No. 1 social networking site in more than 15 countries, including Thailand. A call to the hi5 public relations office in San Francisco was not answered early Tuesday.
A senior Culture Ministry official, Ladda Thangsupachai, said monks should not be banned from using the Internet because they can use it to teach Buddhist philosophy to the young.
"Cyberspace can be very useful for monks," Ladda said. "But it's wrong to use it to pick up girls."