The 26-year-old moved to north London for £8.6m in the recent transfer window, bringing an end to his 18-month stay at La Rosaleda.
"My move happened very fast, so I haven't had the opportunity to say goodbye to fans and teammates," Monreal told reporters.
"I want to thank everyone for a fabulous year and a half and the welcome and treatment I received from everyone at the club.
"I wish Malaga all the best – the club will always be in my heart."
Monreal made his debut for the Gunners in Saturday's 1-0 win over Stoke City.