Janeiro's hotel, where officials from the world's football governing body were also staying.
Last week, police held 11 people and broke up an international gang.
They are accused of illegally reselling tickets, including some originally allocated to players.
Police say the gang earned as much as $90m (£52m) per tournament and could have operated at four World Cups.
The authorities believe some of the tickets were sold to foreign tourists.
Mr Whelan was arrested at the luxurious Copacabana Palace Hotel on Monday.
He was taken for questioning as part of the ongoing police investigation Operation Jules Rimet.
The Switzerland-based Match Hospitality has so far made no public comment on the issue.
As part of the inquiry, police said last week they had identified the first name of the alleged Fifa official from telephone calls.
Fabio Barucke, the investigator in charge of the case, said the official had clearance to Fifa offices, stadiums and other administrative areas where he would have access to match tickets.
The official, Mr Barucke said at the time, was not Brazilian and was in the country only because of the current tournament.
In a statement, Fifa said it "continues to fully collaborate with the local authorities and will provide any details requested to assist with this ongoing investigation".
"Fifa wants to reiterate as mentioned at various occasions its firm stance against any form of violation of the criminal law and the ticketing regulations, and is fully supporting the security authorities in our joint efforts to clamp down on any unauthorised ticket sales."
Among items seized during the arrests last week were 100 tickets, computers, US dollars, mobile phones and documents.
Those arrested could face charges of money laundering, criminal association and illegally selling tickets.
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