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.

Grace Mugabe, 51, was addressing a rally of the governing Zanu-PF party.
Mr Mugabe has governed Zimbabwe since the end of white-majority rule in 1980 following a bitterly fought war.
His wife, who has often professed her undying loyalty to her husband, has assumed an increasingly high profile.
"One day when God decides that Mugabe dies, we will have his corpse appear as a candidate on the ballot paper," Mrs Mugabe told the rally in Buhera, south-east of the capital Harare.
"You will see people voting for Mugabe as a corpse. I am seriously telling you - just to show people how people love their president."
President Mugabe has been backed by his party to stand again in next year's election, but recently cut back on his public engagements.
Grace Mugabe has warned contemporaries of Mr Mugabe from the guerrilla war era that they are not in a position to replace him because they likewise would be too old.
"Anyone who was with Mugabe in 1980 has no right to tell him he is old. If you want Mugabe to go, then you leave together. You also have to leave. Then we take over because we were not there in 1980," she said, gesticulating towards herself.
Last September, the president was rumoured to have died after he reportedly cut short his attendance of an AU summit to fly to Dubai for a health check.
Mr Mugabe later joked about the rumours, saying he indeed died but was only resurrected.
Bulent Mumay found out he was on a list of 42 journalists facing arrest when a friend called him on Monday morning.
[NEXT_CONCEPT]
The wife of Zimbabwe's 92-year-old President, Robert Mugabe, has said that he is so popular that if he died, he could run as a corpse in next year's election and still win votes.