Police have described Whelan as the "facilitator" who allowed a large ring of scalpers to have access to tickets, which they re-sold at vastly inflated prices.
His attorney, Fernando Fernandes, told reporters his arrest was "illegal and absurd."
Whelan, who is based in MATCH's Rio office, will not be allowed to leave Brazil during the tournament. He was detained after the earlier arrests of 11 people, including Algerian national Mohamadou Lamine Fofana.
Police said Whelan was heard on wiretapped phone calls negotiating ticket prices with Fofana, a former player agent whose company is a MATCH Hospitality client.
The MATCH Hospitality subsidiary, which is based in Zurich, paid $120 million for exclusive rights to sell and market more than 400,000 corporate hospitality packages for this World Cup.
In 2011, FIFA extended MATCH Hospitality's exclusive rights through the 2018 and 2022 World Cups without inviting rival bidders.
FIFA hailed that deal — which guaranteed $300 million plus a share of MATCH profits — as one which "further strengthens FIFA's fight against ticket touts."
Trying to distance Whelan from hospitality sales, FIFA and MATCH stressed that Whelan was a director of a subsidiary which has contracts to run accommodation, ticketing and IT services at this World Cup. MATCH Services will also organize hotels for FIFA, media and sponsors at the 2018 World Cup in Russia.
Separately Tuesday, Brazil's federal police said on its website that an Italian and a French citizen, who jointly run a travel agency, were arrested at the international airport in Sao Paulo.
The statement said the two were carrying 48 tickets for the semifinal and final matches — tickets which belonged to "one of the big sponsors" of the World Cup.
Associated Press writer Bradley Brooks in Rio de Janeiro contributed to this report