Calls made and emails sent to Bieber's publicist and agent in Los Angeles weren't immediately returned.
Museum spokeswoman Maatje Mostart confirmed that Bieber visited Friday evening. She said the museum was happy to have received Bieber and didn't see anything offensive in his remarks.
Anne Frank hid with her family in a small apartment above a warehouse during the Nazi occupation of World War II. Her family was caught and deported, and Anne died of typhus in Bergen-Belsen in 1945.
The diary she kept in hiding was recovered and published after the war, and has become the most widely read document to emerge from the Holocaust.
Bieber's whole note read: "Truly inspiring to be able to come here. Anne was a great girl. Hopefully she would have been a Belieber."
Mostart said Bieber called ahead and was given a guided tour.
Bieber's remarks led to criticism from some quarters, as a Facebook response insulting Bieber received more than 1,000 "likes" - slightly more than the museum's original post about the incident.
Meanwhile on Twitter, posts mocking Bieber and imagining that he had visited the museum and walked away thinking only of himself began circulating Sunday, though the message is open to interpretation.
Some of Bieber's 37 million followers also tweeted messages of support. Others in his fan base tweeted that they didn't know who Anne Frank was.
Bieber has had a tough few weeks in Europe. He had to leave a monkey in quarantine after landing in Germany without the necessary papers for the animal. Before that, the 19-year-old singer had a trying stay in London. The star struggled with his breathing and fainted backstage at a show, was taken to a hospital and then was caught on camera clashing with a paparazzo. Days earlier, he was booed by his fans when he showed up late to a concert.
He performed in Arnhem, Netherlands, on Saturday night, and will next perform three nights in Oslo, Norway.