De Villota lost her right eye at Duxford Airfield while testing for Marussia and died a year later aged 33.
The HSE said the driver's family had been informed of its decision.
Manor Grand Prix Racing, which operated Marussia and now runs the Manor team, has yet to comment.
De Villota, the daughter of 1980s F1 driver Emilio de Villota, was injured when the MR-01 race car she was driving hit a support truck on 3 July 2012.
She had been driving at up to 200mph (322km/h), but was travelling considerably slower at the time of the crash.
It was the first time the Spaniard had driven the car for Oxfordshire-based Marussia, which folded in 2014.
Despite losing her eye, she was cleared to drive again in early 2013, but died the following October "as a consequence of the neurological injuries she suffered".
Soon after the crash, Marussia said an internal investigation "excluded the car as a factor in the accident".
An HSE spokesman said: "The investigation is now complete and no enforcement action is being taken.
"Both the company [Manor Grand Prix Racing] and the DP's [deceased person's] family have been informed."
He said HSE had investigated "all reasonable lines of enquiry".
I was due to interview Maria and was standing with her mechanics when she came back in after a test run.
Her car slowed for it to be reversed into the pits, but at the last second it suddenly accelerated again.
By the time it hit the tailboard at the back of a truck, it was doing 30 or 40mph.
I could see the collision impacted directly on her helmet and I feared the worst.
It took almost an hour for ambulance staff to feel confident enough to take her out of the car.
It was an awful moment. I was surrounded by people who knew her very well, including family, friends, engineers and her manager.
Asked whether driver error had caused the crash, the spokesman said it was "not appropriate to disclose".
He added: "However, as with all accidents there are a number of underlying causes."
Speaking in October 2012 after leaving hospital, De Villota said: "I want to keep fighting because I believe so strongly in women being part of motor racing."
No action is to be taken against a former Formula 1 team after test driver Maria de Villota suffered a severe crash in Cambridgeshire in 2012, the Health and Safety Executive (HSE) said.