Aviva estimates the move would wipe around £32 off the typical motor insurance premium and said it would also act as a strong deterrent to "crash for cash" scams, which are based around fraudsters making money by staging a motor accident in order to make false whiplash claims.
Whiplash costs could be almost halved if short-term, minor injuries are not dealt with by cash payments, shaving an estimated £900 million from the current annual £2 billion cost of claims in the UK, the insurer said.
Instead of the typical £2,500 payout that someone gets for a minor whiplash injury claim, they should be offered an assessment of their injuries and treatment to help them recover, it suggests.
More than 475,000 whiplash claims were made in 2013, according to figures from the Association of British Insurers (ABI).
Aviva said analysis of its own claims data shows that 94 per cent of all personal injury claims from a motor accident are for minor whiplash-type injury claims.
It said that in France, for example, it is estimated that whiplash accounts for just three per cent of personal injury claims.
The insurer already offers a whiplash treatment scheme which people making not-at-fault claims for under £10,000 can take up if they want to.
The scheme was launched in 2011 and has helped nearly 7,000 people, with rehabilitation packages including tips on exercises to aid recovery, contact with a physiotherapist and referrals for more specialist treatment in more serious cases.
Aviva suggested that such a service should be extended across the industry to treat all minor whiplash injuries. It would be paid for by insurers and built into a motorist's insurance policy as part of their cover, the insurer suggests.
The industry-wide scheme would cost around £100 million to run, but the savings would amount to around £1 billion, producing a net saving of £900 million which would filter through into everyone's premiums and save the typical motorist £32, Aviva said.
Other ideas put forward by Aviva to help bring premiums down include restricting the use of personal injury lawyers to cases where their expertise is "really needed".
It said legal costs for claims below £5,000 should not be recoverable by a lawyer, instead of the current threshold of £1,000. Aviva said this would save an estimated £11 on the average premium.
It also calculates that banning referral fees for vehicle recovery, car repairs and hire, would save about £7 on the average policy.