A well-known reporter who was sacked from a long-standing job at the liberal Hurriyet newspaper last year, Mr Mumay says the news was a shock.
"It's difficult to be facing such accusations," he told the BBC, "but I wasn't surprised."
Mr Mumay described Turkey's record on press freedom as "troubled".
The country ranked 151 out of 180 in media watchdog Reporters Without Borders' 2016 World Press Freedom Index.
Mr Mumay said he had several journalist friends who had been arrested in recent years.
"I am just a person who practises journalism and describes himself as a critic," he said. "So I am one of those they point the finger at and accuse of being part of the group who planned the coup."
Mr Mumay called on the authorities to look at his social media accounts which would show that he had taken a stand against the coup from the moment he first heard military jets flying overhead.
"Just look on Twitter and you will find several tweets from me strictly rejecting any kind of military coup," he said.
Another name on the list is Fatih Yagmur, an investigative journalist sacked from another liberal daily, Radikal, after writing a story alleging the Turkish government was arming militants in Syria.
In a defiant message on Twitter on Monday, he said that he had no intention of handing himself in to prosecutors, having witnessed torture in Turkish police stations.
Many of the journalists named on the prosecutor's list only found out they were facing arrest when their names were published by the state news agency.
So far only five have been detained, in dawn raids on Monday.
Bulent Mumay found out he was on a list of 42 journalists facing arrest when a friend called him on Monday morning.