Mahsa Amini, 22, died on Friday, days after eyewitnesses said she was beaten in a police van in Tehran – allegations denied by police.
Some women at the ceremony reportedly removed their headscarves in protest at the compulsory wearing of hijabs.
Mourners chanted “death to the dictator”, with videos showing police later firing on a crowd.
The funeral took place in Ms Amini’s hometown, Saqez, in the western province of Kurdistan.
According to videos published on social media, locals gathered very early in the morning to prevent Iranian security forces rushing through the burial in secret to avoid protests.
Reports suggested that some angry protesters marched toward the local governor’s office to protest about the death. According to videos received, the security forces opened fire on protesters.
There were also reports of injuries and arrests. In videos published on Twitter, security forces can be seen guarding the governor’s office and arresting protesters trying to get close to the building.
A picture of Ms Amini’s gravestone was published on social media. It reads: “You didn’t die. Your name will be a code [rallying call].”
Ms Amini was arrested on Tuesday by the morality police for allegedly not complying with the strict dress code on head coverings.
According to eyewitnesses, she was beaten while inside a police van and slipped into a coma later.
Iranian police denied the allegations, saying she had “suffered a sudden heart failure”.
Ebrahim Raisi, Iran’s hardline president, has asked the ministry of the interior to launch an investigation into the death.
Kasra Hospital in Northern Tehran said in a statement that Ms Amini was admitted on 13 September showing “no vital signs”.
The statement was later removed from the hospital’s social media after hardline social media accounts accused hospital staff of being “anti-regime agents”.
Credit: Facebook / Sola Omoniyi