The Many Saints of Newark explores the early life of mobster Tony Soprano, played in the show by James Gandolfini.
Gandolfini's real-life son Michael plays the young Tony, and one reviewer said it is a "wonderful" performance.
In the opinion of another, however, Alan Taylor's film "provides little in the way of fresh illumination".
Writing in the Hollywood Reporter, critic David Rooney also said he felt the young Tony "remains a bystander in his own origin story".
The older Gandolfini, who died in 2013 at the age of 51, played mob boss Tony in six seasons of the New Jersey-set crime saga, which ran from 1999 to 2007.
The film, which came out in UK cinemas on Wednesday, sees the teenage Tony come under the influence of career criminal Dickie Moltisanti during the 1960s Newark race riots.
The Telegraph's Tim Robey praised the "compelling ambivalence" that Alessandro Nivola brings to Moltisanti, whose surname means Many Saints in English.
Robey's four-star review called the film "a rich imaginative leap into the pre-history of an iconic show, and a rare instance of the big screen doing right by the small".
The film also received four stars out of five from The Independent, whose critic Clarisse Loughrey called it "fierce and brilliant".
She too hailed Nivola for the "ferocious magnificence" of his portrayal of "a man wrestling with his own monstrosity".
More praise came from Empire's Nick De Semlyen, who called the film "a satisfying standalone" that would make fans of the series "shiver with delight".
Total Film's James Mottram expressed similar sentiments about a "blistering" prequel that he described as "gripping, darkly funny and deeply human".