The romantic drama, which debuted at the Venice Film Festival in September, sees Argo star Affleck play a man who finds himself torn between a woman who has moved to the US to be with him (Kurylenko) and an old flame (Rachel McAdams).
The trailer is accompanied by a voiceover from Javier Bardem's character, a priest who starts to question his faith.
Malick's previous film The Tree of Life won the Palme d'Or at the Cannes Film Festival in 2011 and was nominated for three Oscars.
The filmmaker is currently working on Knight of Cups and a project based around the music industry. The interlinked movies will both feature Christian Bale, Natalie Portman and Cate Blanchett.
To the Wonder, Malick's seventh feature, will open in the UK on February 22, 2013.