The 'Transformers' actor - who was first romantically linked with the singer last September - is taking time apart from the 31-year-old musician because she wants to focus on her 'Madalene' world tour.
A source told E! News: ''They have been taking time apart since May, because of her work schedule.
''They both have put their relationship on hold. 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.''
According to the insider, since the split, communication between the former couple has been ''very minimal''.
The source added: ''It's been rocky between them for a month now.''
Prior to their relationship, the 32-year-old actor married Mia Goth in 2016 after meeting on the set of 'Nymphomaniac' but it was confirmed they had split shortly before he was linked with Twigs.
His representative previously said: ''Shia and Mia have filed for divorce. The separation is amicable and all details pertaining to the divorce proceedings will remain private.''
The 'Lawless' star had previously credited the actress for making him less ''cynical'' about marriage.
He said: ''You always hear these people who are all cynical, like, 'Ah, man, once you get married everything changes'. But for the better though!''
Twigs - whose real name is Tahliah Debrett Barnett - was engaged to marry 'Twilight' actor Robert Pattinson ,33, but the pair called things off after three years together in late 2017.
An insider said that Robert was ''tired'' of being unable to spend time with his ex-fiancee.