The plaintiffs are the heirs of Ed Townsend, a musician and producer who co-wrote Gaye's 1973 soul classic.
They allege that there are “striking similarities and overt common elements” between Gaye's sultry classic and Sheeran's Thinking Out Loud.
It is not the first time Sheeran has been taken to court, as copyright lawsuits in the music industry flourish.
Sheeran gave evidence in a London court in April last year in a case centred around his song Shape of You. He is among the potential witnesses to be called in this trial as well, in which opening arguments were due to begin on Tuesday after a jury is selected, a lawyer working on the case told AFP.
Townsend's family has pointed out that the group Boyz II Men has performed mash-ups of the two songs, and that Sheeran has blended the songs together on stage as well.
Sheeran's team contests the allegations, saying “there are dozens if not hundreds of songs that predate and postdate” Gaye's song, “utilising the same or similar chord progression”.
“These medleys are irrelevant to any issue in the case and would be misleading [and] confuse the jury.”
Sheeran's Thinking Out Loud shot up America's Billboard Hot 100 charts when it was released, and won Sheeran a Grammy Award for Song of the Year in 2016.
The lawsuit, filed in 2016 — and refiled in 2017 after being rejected on procedural grounds — also names Sony.
In Sheeran's London trial, the singer called the lawsuit emblematic of copyright litigation that goes too far, potentially stifling creativity.
The judge agreed, declaring that Sheeran had “neither deliberately nor subconsciously copied” part of the melody in the song Oh Why by Sami Chokri and Ross O'Donoghue.
The judge acknowledged similarities between the two songs, but ultimately ruled there were large differences, and that Chokri's lawyers failed to prove Sheeran had ever heard the song.
Gaye's family is not part of the New York lawsuit against Sheeran, though his estate successfully sued the artists Robin Thicke, Pharrell Williams, and T I over similarities between the song Blurred Lines and Gaye's Got to Give it Up.