The Muslim Council of Britain (MCB) said mosques would offer refreshments and "insight" into how they run.
Leaders from other religions have also been invited, to "demonstrate unity".
The MCB has raised concerns about anti-Muslim sentiment since 17 people were killed by Islamist militants in Paris last month.
Announcing Visit My Mosque Day, the MCB said: "Mosques will be sharing tea and refreshments alongside an insight into the day-to-day goings on of a busy Muslim centre of worship.
Members of the Muslim community "may be on hand to answer questions about Muslims and Islam where this is possible," it said.
"Local mosques will also be inviting inter-faith leaders as well, and all will be invited to come together to demonstrate unity and solidarity during what has been a tense time for faith communities."
Speaking outside the East London Mosque in Whitechapel, MCB assistant secretary general Miqdaad Versi said the organisation wanted to "de-mystify what Islam, Muslims and mosques are all about".
"People can have the opportunity to understand these things directly from people that they can speak to, and by actually experiencing these institutions and coming into mosques they can break down the barriers that they previously had," he said.
Mr Versi said there had been a rise in "Islamophobia" since the Paris killings, with attacks on three or four mosques, more verbal attacks against Muslims and "a lot more hate mail" being received by the MCB.
"For us it's important to try and create a positive image, and not let the actions of a few impact the reality of the many," he added.
The Reverend Fred Ashford-Okai, one of those who visited East London Mosque earlier, said: "The more we know about each other - Muslims, Christians, Jews, even those with no faith - the more we can actually live a more cohesive life in our community."
More than 20 mosques were expected to take part.
The figure is a small proportion of the total number of mosques in Britain, which is estimated to be 1,750.
The MCB said only 55-60% of mosques were affiliated to it, and the total includes small establishments such as prayer rooms in schools and offices.
Mosques have opened their doors to the public as part of a drive to "reach out to fellow Britons following tensions around terrorism".