Sgt Emile Cilliers, 35, from South Africa, was questioned by police last week after his wife Victoria fell 4,000ft (1,219m) over Wiltshire on 5 April, the Press Association said.
Wiltshire Police described 39-year-old Mrs Cilliers' survival as "miraculous".
However she suffered "multiple serious injuries".
Her main parachute failed to deploy, while her reserve chute only partially opened - enough to slow her descent.
Det Insp Paul Franklin said she was an experienced parachutist but had "very nearly lost her life" in what should have been a "routine" jump.
"This woman would have been dead if her chute hadn't partially opened, this meant her descent was slowed enough for her to survive the fall," he said.
An investigation was launched after the parachute club at Netheravon Airfield, in Salisbury Plain, alerted police to concerns over what had happened.
Detectives said "slinks", or soft links, used to connect the canopy to the parachute harness, were "missing" and they were particularly keen to find them.
Mrs Cilliers, from Amesbury, was taken to Southampton General Hospital with "multiple fractures throughout her body" and was now recovering at home, police said.
Her husband, an Army corps training instructor, was bailed last week.
A man held on suspicion of attempted murder after his wife's parachute failed to open during a skydive is a British Army sergeant, it is reported.