The "Transformers" star and British singer were first linked last September (18) - shortly after the actor's split from wife Mia Goth - and went public with their relationship with a passionate display in Los Angeles in November.
However, sources have told E! News that the couple "have been taking time apart since May, because of her work schedule." Twigs, real name Tahliah Debrett Barnett, is currently in the middle of her "Magdalene" world tour.
"They both have put their relationship on hold," the insider added. "FKA has been focusing on her tour and she wanted to put all of her heart and soul into it. They are really up in the air right now and were waiting until all of her work commitments were fulfilled to figure it out."
While a potential reunion in the future isn't out of the question, the source revealed that "communication (between the pair) has been very minimal," and added, "It's been rocky between them for a month now."
Reports of the pair's break come as Shia was spotted cuddling up to a mystery brunette at Kanye West's Sunday Service last weekend, June 02.
An eyewitness described the woman as "being cuddly towards him at one point in the service," and added, "They seemed more than friends and it definitely seemed like they knew each other well."