The 60-year-old man suffered a broken hip and wrist during the incident at The Glades shopping centre in Bromley, south-east London, on 22 December.
He subsequently suffered further health complications and remains critically ill in hospital.
A 30-year-old woman arrested on suspicion of grievous bodily harm was released on bail until 29 January.
Broken hip and wristThe Metropolitan Police said they were called to a store in The Glades shopping centre in Bromley at 13:00 GMT on 22 December, to reports of a man injured during an altercation.
A spokeswoman said: "It is understood that the man was struck with a trolley after being pushed by a woman.
"He fell to the ground and sustained injuries, including a broken hip and wrist, and was taken to a Kent hospital for treatment."
She said that on Boxing Day, officers were told the man had suffered further health complications and he was now in a critical condition.
"Officers subsequently arrested a 30-year-old woman on suspicion of GBH," she said.
A spokesman for M&S confirmed an incident took place at their Bromley store on 22 December and that they were helping with the police investigation.
