Jones, 21, suffered a fractured leg and had arteries and nerves exposed, WWL-TV reports.
Per WWL, this is how the story started:
WWL.com columnist Jeff Palermo talked with Jones' father, who was headed to the hospital. Alfred Jones confirmed his son was hurt, but said he was alert when paramedics took him to the emergency room.
New Orleans EMS reported transporting a patient from the scene of the crash in guarded condition.
Jones was listed in critical condition and had a surgery scheduled for 10:15 a.m.
Jones, a third round pick, had already signed his contract with the Giants. He played baseball at LSU and was drafted by the Brewers.