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."

20 January 2016 Last updated at 12:03 GMT
It had been stuck on the side of the mountain in Snowdonia, Wales, for days and couldn't move from its dangerous position on the ledge.
A rescue team from the RSPCA had to lower themselves down the mountain using ropes to reach the sheep, who was then lowered down with them, to the bottom of the cliff.
They said that the sheep wasn't injured but was very hungry after its cliff-side adventure.
Pictures and video courtesy of RSPCA Cymru.

The 77-year-old man, from Newhaven, and the woman, from Lewes, were on the A259 at White Rock when the accident happened on Thursday evening.
They and the motorcyclist were taken to the Conquest Hospital in Hastings, where the man later died.
Police said the 22-year-old motorcyclist, from St Leonards, and the woman were not detained.
Sussex police are appealing for witnesses to the accident, which happened just after 21:00 BST on Thursday.

Schools and businesses were shut and airport services suspended, as the cyclone made landfall with heavy rain and winds of up to 140km/h (85mph).
Teams from the army and National Disaster Relief Force, along with two naval ships, are on standby.
Fishermen in Andhra Pradesh and Tamil Nadu have been warned not to go to sea.
Police said disaster management teams had evacuated more than 15,000 people from low-lying areas.
The Tamil Nadu state government said in a statement that 260 trees in the city had fallen as a result of strong winds. Parts of the city have also been flooded.
Winds were so strong that glass panels were torn from the facade of Chennai's Hyatt-Regency hotel.
YK Reddy, director of the meteorology department in Hyderabad, told BBC Hindi the storm would weaken after making landfall.
The storm comes about a year after Chennai experienced devastating floods which killed 70 people.
In December 2011, more than 30 people died and many homes were damaged after a cyclone struck near the town of Pondicherry.
And in May 2010 at least 23 people died as a powerful cyclone caused widespread havoc across Andhra Pradesh.
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.
[NEXT_CONCEPT]
A sheep trapped on a ledge on the side of a cliff has been rescued.
[NEXT_CONCEPT]
A man died and a 90-year-old woman was injured in a collision with a motorcycle on a busy road in Hastings.
[NEXT_CONCEPT]
At least seven people have been killed and thousands evacuated from coastal areas in two southern Indian states, as Cyclone Vardah lashed Chennai (Madras).