The YouGov poll for press agency DPA found that 62 percent of people said that they didn't count a single Muslim among their close personal friends.
But that may be in the process of changing, as around half of young people aged 18-24 said that their social circles included Muslims.
Pollsters also found that the number of Muslim friends a person had was closely linked to their level of education.
Among those who had graduated from high school with the Abitur academic qualification, 42 percent said they had Muslim friends.
But just 28 percent of people who had finished their schooling with only a secondary education certificate could say the same.
“Our own surveys also show that higher levels of education go along with greater openness to diversity,” said Cornelia Schu, an expert with the German Foundations for Integration and Migration (SVR).
People with higher income also “generally tend to have a more positive attitude towards people with a migration background,” Schu said.
Fear and suspicion
Public anxiety about Islam has led to increasing calls from politicians in recent weeks to police the religion and its followers.
Chancellor Angela Merkel's Christian Democratic Union (CDU) called recently for state surveillance of preachers in all mosques to make sure they weren't spreading radical ideas.
Alternative for Germany leader Frauke Petry holds up her hand to vote at the party's convention. Photo: DPA
And right-wing populist party Alternative for Germany (AfD) has made a ban on minarets, the Muslim call to prayer and full-face veils a key part of its policy platform.
Little knowledge of Islam
More than half of non-Muslims surveyed said that they didn't have much idea about the content of the Muslim religion, while one in five said they knew nothing at all about it.
What's more, 84 percent of non-Muslims said they had never been inside a mosque in Germany – although mosques have been holding open days since 1997 in a bid to boost understanding.
By contrast, 68 percent of Muslims said that they had good or very good knowledge about Christianity.
Around 60 percent of non-Muslims said they had noticed an increased number of Muslims in their everyday life, but most did not report encountering radical minorities.
Germany is home to more than four million Muslims. Many arrived in the late 20th Century as so-called “guest workers” - or are relatives of those same migrants.
Some also arrived as refugees from countries such as Afghanistan, Iran, Syria and Iraq, while there is a small minority who have converted to Islam.
Most Muslims live in western Germany, with only two percent living in the states making up the former German Democratic Republic (GDR) before the refugee crisis began in 2015.
The YouGov pollsters surveyed a representative sample of 2020 adults between April 25th and 27th.