Critically and commercially successful on release, it was nominated for the Academy Award for Best Picture, Best Original Screenplay, Best Actor for Adam Driver and Best Actress for Scarlet Johansson, while it won the Best Supporting Actress Academy Award for Laura Dern.

Critical reviews for the film were generally positive with Owen Gleiberman of Variety writing “At once funny, scalding, and stirring, built around two bravura performances of incredible sharpness and humanity, it's the work of a major film artist, one who shows that he can capture life in all its emotional detail and complexity — and, in the process, make a piercing statement about how our society now works”, while Jon Frosch of The Hollywood Reporter noted that "Other American films about divorce have portrayed this phenomenon — the legal process driving and shaping the couple's feelings rather than vice versa — but none with the force and clarity of this one [...] It's also funny and, when you least expect it (and most need it), almost unbearably tender, thanks in large part to the sensational leads, who deliver the deepest, most alive and attuned performances of their careers.”

Marriage Story was chosen by the American Film Institute, the National Board of Review, and Time magazine as one of the ten best films of the year.

Today, it stands on Rotten Tomatoes at 94% with its critical consensus reading: “Observing a splintering union with compassion and extensive grace, the powerfully acted Marriage Story ranks among writer-director Noah Baumbach’s best works.”