Managers of the Hammersmith Apollo, now called the Eventim Apollo, made the decision to evacuate when they were told of the threat.
Eghbali, an exiled Iranian singer with a large international following, was due to appear at his first London concert in seven years.
Evacuated concertgoers stayed at the famous venue, chanting “one solution, revolution” and “woman, life, freedom” — slogans which have been shouted at protests in Iran.
It is not known who made the call to police, or why.
“Police received an anonymous call making a threat towards a music venue which officers subsequently determined as likely to be the Eventim Apollo,” London’s Metropolitan police said.
“There was nothing to indicate that the threat made was genuine but at 20:21 officers attended the venue to speak to security staff and to determine whether they were aware of anything suspicious.
“Nothing of suspicion had been fund but at 20:40 the venue management took the decision to evacuate as a precaution.”
There were no reports of injuries and no suspicious items were found, police added.
At the weekend protests continued across Iran — the latest rallies following the death of Mahsa Amini in police custody.
Two more people died, a general strike was staged and the internet was blocked.
Amini was a 22-year-old Iranian Kurdish woman who died in custody on September 16, three days after she was arrested in Tehran by the country's notorious morality police for an alleged breach of the country's strict dress code for women.
Demonstrations have continued despite internet restrictions to prevent gatherings and a violent clampdown that has claimed more than 150 lives, according to human rights groups.
Eghbali, 71, is “one of the most well known and loved Iranian singers of all time”, according the Apollo. He was born in Tehran but spent his early years in Kurdish regions of the country.
The London concert was to have been his first stage event in London for seven years.
In July, a conference of Iranian exiles fighting for democratic change at home was cancelled after a security threat.
The Free Iran World Summit, due to be held in Durres, Albania, was postponed until further notice.
The US embassy in Tirana had warned the previous day of “a potential threat targeting the Free Iran World Summit and advised US citizens to avoid the event.