The teaser, which is set to air during Super Bowl 50 on Sunday, is narrated by Rickman's character, the Blue Caterpillar, and tells a dark story of what has happened to Wonderland in Alice's (Mia Wasikowska) absence.
"You've been gone too long, Alice," Rickman's voice intones with the dire gravitas only he could ever fully embody. "There are matters which cannot be neglected."
Alice Through the Looking Glass, Disney's sequel to their 2010 hit Alice in Wonderland, follows the eponymous heroine as she returns to the surreal world of Wonderland in an attempt to save her friend, the Mad Hatter (Johnny Depp).
The film was Rickman's final project before his death. The late actor also stars in the upcoming military drama Eye in the Sky, opposite Helen Mirren and Aaron Paul, which comes out Mar. 11.
"Alan was a towering person, physically, mentally and as an artist," the 70-year-old actress said. "He was utterly distinctive, with a voice that could suggest honey or a hidden stiletto blade, and the profile of a Roman Emperor. He was also a great friend, generous and social. He will be very missed by many."