The protesters were planning to march through the square to Gezi Park, the BBC reported. The area has been the site of large demonstrations for several weeks.
Huseyin Avni Mutlu, Istanbul's governor, said he had ordered police to block access to the square, the Turkish newspaper Hurriyet reported.
"The Constitution says that anyone can stage a demonstration without giving notification, but the legislation says that applying to the authorities for permission is mandatory. So nobody can say they exercise their constitutional rights. This is unlawful," Mutlu said at a news conference.