Björn Söder, who is also a Deputy Speaker in the Swedish parliament, wrote the comment on Facebook after 12 people were killed in the Charlie Hedbo offices in Paris earlier this week.
On Friday morning, the Dagens Nyheter newspaper reported that Swedish MP Veronica Palm of Prime Minister Stefan Löfven's Social Democrat party had reported Söder to the police for racial agitation (hets mot folkgrupp).
"It's not legal to offend people based on their race, and I think this should be treated as racial agitation," she told the paper.
Others have also chimed in on the Facebook post, including political scientist Olof Ruin, who said it was "an embarrassment for Sweden".
While Söder's initial comment read "the religion of peace shows its face", Dagens Nyheter said he then edited the post to add a question mark at the end and later deleted it.
"As far as I know there was always a question mark after the post," Sweden Democrat press spokesman Henrik Vinge told The Local on Friday afternoon.
"But it is not a serious matter, this is about political point scoring by a Social Democrat politician," he added.
"In these times where freedom of speech is threatened, politicians should not be seeking to silence each other."
He said that Söder had not been questioned by police and that he did not expect him to be, arguing he felt that criticism of the Facebook post had been "overblown".
When questioned about whether he understood why some Muslims could be offended by the comment, he said: "Muslims should try to create a force to prevent this [extremism] from happening. We all have a responsibility to prevent extremism."
The Sweden Democrats earlier condemned the Paris massacre in an official statement, calling it "an attack on all of Europe and on the values of democracy and freedom of speech."
The party has roots in the country's most radical extreme right and entered parliament in 2010 with the ambition of curbing the Nordic country's generous policy on immigration and refugees. It is now the third largest group in the Swedish parliament, scoring almost 13 percent of the vote in the last general election in September 2014.
Björn Söder previously came under fire from Sweden's Jewish community
in December when he told Swedish newspaper Dagens Nyheter that Jews could not be considered Swedish unless they abandoned their religious identity.
Söder's Facebook comment follows a string of attacks in Sweden recently that some say reflects the country's growing Islamophobia. Over the Christmas break, three separate mosques across the country caught fire, prompting pro-Muslim rallies across the country last week. Another mosque was vandalized in southern Sweden this week.
Mohammed Fazlhashemi, Professor of Islamic theology and philosophy at Sweden's Uppsala University, told The Local on Thursday that he thinks Sweden may see even more attacks.
"When it comes to what happened in Paris, I think we may see reprisal attacks in Sweden. The risk is definitely there, and I think the worry is there among Sweden's Muslims," he said.
"The mosque attacks in Sweden haven't come out of the blue, we've seen Islamophobic rhetoric gradually strengthening in Swedish society, and the effect has been that Muslims here are mistreated."
Sweden Democrat press spokesperson Henrik Vinge told The Local on Friday that he believed Sweden's mainstream political parties had been "ignoring the need to discuss multiculturalism" for many years.
Björn Söder's post came as other nationalist leaders around Europe also faced criticism for their response to the Paris shootings.
In the UK, Ukip leader Nigel Farage said the attack on Charlie Hebdo was "truly horrific," adding that it raised questions about what he called a "gross policy of multiculturalism".
Farage told British news network Channel 4 News there was a "very strong argument" that the events were a result of "a fifth column" which he said lived in Paris and London.
"We've got people living in these countries, holding our passports, who hate us," he said.
The leader of the UK's junior coalition party the Liberal Democrats was among the most vocal critics of his comments. Nick Clegg stated on a radio phone-in that he was "dismayed that Nigel Farage immediately thinks, on the back of the bloody murders that we saw on the streets of Paris…his first reflex is to make political points."
In France, a huge row broke out on Thursday after the National Front party was not invited to a rally to remember the Paris shooting victims on Sunday.
Former French Prime Minister François Fillon said: “"Our best response is the total unity of the country. We can't have any dissenting voices.”
“It’s a mistake, we should unite everyone and not judge people by their political colours,” Imam Farid Darrouf told The Guardian newspaper.
“Everyone should participate to say no to this barbarism. Division can only feed the fanatics.”