He was seized on Wednesday and taken to an immigration detention centre in the city, Sweden's Expressen newspaper reported on Thursday.
Abdel-Nasser el Nadi, chief executive of Vetenskapsskolan, is the fifth senior member of Sweden's Muslim community to be placed in custody in less than a month.
Three prominent imams are now in custody: Abo Raad, imam of a mosque in Gävle, Hussein Al-Jibury, imam of a mosque in Umeå, and Fekri Hamad, imam of a mosque in Västerås. Raad's son is also being held.
Sven-Erik Berg, the school's headmaster, told The Local that he had no idea what was behind the arrest.
“We don't know anything. I don't know anything more than you,” he said. “We are doing nothing, but the school is naturally maintaining a dialogue with the Swedish School Inspectorate and their lawyers.”
He said it was inaccurate to describe the school as a 'Muslim school' as it has no official confessional status.
“The chief executive is a central person among Swedish Muslims, so naturally the group of people we recruit from are often those who have a relation to Islam or Sweden's Islamic associations,” he said. “But the school does not go around telling children what they should or shouldn't believe.”
On its website the school declares: “At our school everyone is treated equally irrespective of gender, religion, ethnic background, appearance, opinions, or abilities”.
“We are one of the best schools in Gothenburg. You just have to look at the statistics,” Berg added.
A spokesman for Säpo told Expressen that he could not comment on any of the five cases or on whether they were in some way linked.
But according to the Swedish news site Doku, which investigates Islamic extremists, Säpo is probing whether el Nadi has any links to a network of Islamic militants.
In an article published last October, the site alleged that El Nadi's activism was part of the reason that so many young men from Gothenburg had travelled to fight for the terror group Islamic State in Syria and Iraq.
El-Nadi was previously the school's headmaster, and the school was in 2018 criticised by the Swedish School Inspectorate for not sufficiently promoting equality between girls and boys.
When he was interviewed by Dagens Nyheter a year ago, he asserted his loyalty to Sweden.
“I have five children, all of whom were born in Sweden, a big family, and I want to protect this society in the same way that I have protected my children,” he said.
El-Nadi was born in Egypt but has lived in Sweden since 1992. He has twice applied to become a Swedish citizen, in 2007 and 2011, and twice been rejected.