It is up for six Razzies - including worst picture, worst director, worst actor and worst actress.
Jupiter Ascending, Pixels, and Paul Blart: Mall Cop 2 also have six nods each for the Golden Raspberry Awards, to be announced next month.
The awards launched in 1980 as a spoof of the Oscars.
Nominees for the Razzies have been named the day before the Oscars shortlist is announced.
Superhero film Fantastic Four, sci-fi adventure Jupiter Ascending, comedy Paul Blart: Mall Cop 2 and Adam Sandler's video game film Pixels complete the line-up for worst picture.
Fifty Shades of Grey, the film version of EL James' erotic novel detailing the sadomasochistic affair between student Anastasia Steele and billionaire Christian Grey, is also nominated for worst screenplay.
Its stars Dakota Johnson and Jamie Dornan are cited for worst screen combo.
Sam Taylor-Johnson, nominated as worst director, has since pulled out of directing its planned two sequels. The next Fifty Shades film is due for release next year.
Sandler is Razzie-nominated for a fifth consecutive year and could pick up awards for worst actor, for Pixels and The Cobbler, and worst screen combo, for "Adam Sandler and any pair of shoes" in the latter film.
Eddie Redmayne, tipped for an Oscar nomination for his role in The Danish Girl, is in contention for worst supporting actor for playing villain Balem Abrasax in Jupiter Ascending.
Mila Kunis and Channing Tatum are nominated for worst actress and worst actor for the Andy and Lana Wachowski-directed film.
Oscar-winner Gwyneth Paltrow gets a worst actress nod for comedy heist Mortdecai - with co-star Johnny Depp scoring two nominations, for worst actor and worst screen combo for his partnership with his glued-on moustache.
It isn't all bad news for the nominees however, with the Razzie Redeemer Awards rewarding previous Golden Raspberry recipients who have gone on to do good work in the past year.
Nominees for that prize include Sylvester Stallone, for his Golden Globe-winning role as Rocky Balboa in Creed, director Elizabeth Banks for Pitch Perfect 2, M. Night Shyamalan for directing horror film The Visit and Will Smith for Concussion.
The winners will be announced in Hollywood on 27 February - the day before the Oscars ceremony - having been voted for online by around 900 members of the Razzies committee.
Those "honoured" for the worst films of the past 12 months will win a gold spray-painted trophy worth $4.97 (£3.44) if they bother turning up - but unlike the Oscars, the winners usually stay away.
Sandra Bullock is among those who have attended the ceremony - showing up with DVDs of All About Steve to hand to the audience after being named worst actress in 2010.

The 22-year-old will have an operation in two weeks, which is expected to sideline him for nine months.
Brentford have not disclosed the full details of the injury, which was sustained during their victory against QPR on Friday.
Macleod was stretchered off in the 87th minute of Brentford's 2-0 win at Loftus Road, having come on as a substitute.
The former Scotland Under-21 international was previously ruled out for a year because of various injuries after he joined the Championship club from Rangers in January 2015.
The contenders for the worst films of the year have been announced, with Fifty Shades of Grey dominating the nominations.
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Brentford midfielder Lewis Macleod will require reconstructive knee surgery and has been ruled out for the season.