A photo of Stephen Leyland, 64, appears in Rumiyah alongside a caption that encourages supporters to take “even the blood of a merry Crusader citizen selling flowers to passersby”.
Rumiyah also lists businessmen on their way to work, teenagers playing sports and old men buying lunch as “fair game”.
Counter-terrorism police have interviewed Mr Leyland after the magazine emerged online.
“It has come as a bit of a shock,” he told The Times. “When I was first contacted I thought it was a wind-up.
“I really don’t know what to do. I’m not scared but I am concerned that the photo is in this magazine.”
The image of the florist is believed to have been lifted from the internet.
Mr Leyland, from Cheshire, added: “I don’t know any jihadis.
“My customers are the Alderley Edge crowd, footballers’ wives and those sort of people.
“They (counter-terrorism police) said that the Foreign Secretary had asked about it.”
It comes less than a fortnight after IS released a video which purportedly shows a British boy killing a prisoner in Syria.
The first edition of Rumiyah, published on Monday, also called on jihadis to target Melbourne and Sydney.
Australian Prime Minister Malcolm Turnbull said it was a “disturbing reminder” of the threat of a terror attack in his country.
He said: “The capacity of Daesh, of course, is much less than they proclaim it to be but we do have to be very alert to the actions of these lone actors.
“Every time there is a terrorist incident, wherever it is in the world, we learn as much as we can about it and then take those learnings to keep Australians more safe.”
Officials say they have stopped 10 terror attacks in Australia in the last two years.
News Source SkyNews