The two sides had played out a 2-2 draw at La Rosaleda when the trouble began, with a stoppage-time penalty awarded for handball against Fulham captain Calvin Bassey allowing Eneko Jáuregi to convert and level the match in the 90th minute.
Arbeloa, the former Real Madrid defender now in charge of Fulham, confronted Spanish referee Ortiz Arias in the aftermath and was shown a straight red card following the disagreement.
With the match finishing level, the contest was due to be settled on penalties, but Fulham refused to take part. A member of Arbeloa's coaching staff, asked by supporters in the stands, explained that the shootout had not been written into the match contract, and Málaga sources later said Fulham had also cited the risk of missing their flight back to England if the game ran any longer.
The match was therefore awarded to Málaga, who were declared champions of the trophy without a shot being taken in the shootout.
Ryan Sessegnon had given Fulham an early lead in the 24th minute, only for Málaga to respond four minutes later. Kelechi Iwobi restored Fulham's advantage in the 57th minute before Jáuregi's stoppage-time penalty completed the comeback and forced the walkover in Málaga's favour. The result meant a smooth pre-season send-off for a Málaga side preparing for their return to Primera División, while the walkover added an unwanted footnote to an already eventful start for Arbeloa in English football since taking charge of Fulham.
The Spaniard's dismissal capped an ill-tempered finish to what had otherwise been a competitive friendly between the two clubs, played in front of a crowd of more than 17,000 at La Rosaleda ahead of the new domestic seasons in both countries.
Neither club has since commented further on the shootout dispute beyond confirming their differing accounts of what was agreed in the pre-match contract. In a symbolic gesture after Fulham's players left the pitch, Málaga's squad urged Jáuregi to take one final unopposed spot-kick, which the crowd celebrated as though it had settled the trophy officially.