Speaking to tabloid Blick, Atef Sahnoun, a member of the An'Nur association, said it would move out of the building after the month of Ramadan and the association would be dissolved.
The closure of the mosque has been on the cards for some time, since the landlord of the building last year refused to extend the association's rental contract, which is due to expire.
Sahnoun told Blick they had been unable to find new premises.
The mosque has also had financial problems and is leaderless, with no one willing to take on the presidency, said the paper.
But public pressure may also have contributed to the closure of the mosque since it became the subject of allegations of radicalization and hate speech.
In 2015 preachers at the An'Nur were accused by a Swiss journalist of meeting with young people in a bid to radicalize them, allegations denied by the imam.
In June 2016 police arrested a man with close ties to the mosque who was thought to be a key figure behind the radicalization of young Muslims in the area.
And in November of that year police raided the mosque and made several arrests after a tip off about an imam who gave a sermon in which he called for Muslims who do not partake in communal prayer to be murdered.
In February this year police arrested ten people suspected of attacking the two members of the mosque who allegedly tipped off a journalist about the controversial sermon.
Winterthur is considered a hotspot for Islamic radicalization in Switzerland with at least five young men having left the city to travel to Iraq and Syria to fight for Islamic State.