Suspect had been under surveillance by security operatives.
His wife says that he will be tortured if he is returned to Algeria.
Funding is said to have been raised from human trafficking.
The two Algerians were part of a cell, under investigation since 2017, which was planning an attack with explosives in Barcelona.
Harrak maintains that he was in fact supplying information to the National Intelligence Centre.
There was a minute's silence across Majorca yesterday. Immediate security measures include concrete barriers that have been installed in the Plaça Porta Pintada.
The announcement of more summer flights was "unacceptable"; accommodation problems were affecting the police; Majorca was silent for a minute on Thursday.
Terrorism is the number-one concern for British holidaymakers. Travel industry bosses say terror attacks have had the greatest impact on their business in the past year.
Since Spain was placed on level four terrorist risk alert last year, 156 supposed jihadists have been detained.
Three of the Big Four Majorcan hotel chains pulled out of Tunisia and have no plans at present to return.
Security forces in the country are stepping up their vigilance, with tourist areas and religious sites being particularly sensitive.
It was just before 8am on Tuesday when the national interior ministry tweeted a message that announced the arrest in Palma of a Moroccan national with close relations with DAESH.
Pilar Costa spoke of the need for calmness and for trust in the security forces in light of the arrest of the IS suspect, Mohammed Harrak.
Harrak had said that the Paris attacks had represented an "excellent day", one that made "Europe tremble".
Mohammed Harrak refused to make a statement claiming it was a "big misunderstanding".
Spanish airports agency cancels all flights to Brussels. There were people from Majorca at the airport but it is unknown if anyone from the island has been a casualty.
The plane was travelling from Athens to Madrid when the pilot requested activation of the anti-terrorist protocol.
Voicing her own support for the French people, President Armengol said that terrorists "will not defeat democracy".