Advertising will no longer state that the drugs are remedies for ailments such as coughs and colds, only that they can relieve acute and moderate pain that is not relieved by paracetamol, ibuprofen or aspirin alone.
Any references to painkilling power and strength will also need to be removed as part of the changes to the advertising and promotion code of practice for manufacturers and retailers.
The updated advertising controls come as part of new guidelines devised by the MHRA for the sale of over-the-counter medicines that contain codeine and dihydrocodeine (DHC), such as Nurofen Plus and Solpadeine Plus.
The new guidelines aim to minimise the risk of overuse and addiction as official figures show that more than 30,000 consumers have become addicted to the painkillers, many accidentally.
The MHRA said that from next year, changes would be made to the packaging of these over-the-counter painkillers.
Clear and "prominently positioned warnings" will be placed on the packet's label and patient information leaflet, explaining the risk of addiction and the importance of not taking the medicine for longer than three days.
This includes the inclusion of the statement: "Can cause addiction. For three days use only"
Packs will be limited to just 32 tablets, with larger packs available only by prescription.
Dr June Raine, MHRA director of vigilance and risk management of medicines, said that taken in the correct manner and for the right purposes, codeine and DHC are very effective and acceptably safe medicines, but said that they can be addictive.
Raine said: "The MHRA is ensuring that people have clear information on codeine containing medicines on what they are to be used for and how to minimise the risk of addiction.
"Anyone who has concerns should speak to their pharmacist or a doctor."
The MHRA's action is being taken in parallel with the Department of Health's review of policy on addiction to prescription and over-the-counter medicines.