The incident happened in Blackheath Road near Deptford Bridge at around 11.20am today (December 29).
Officers arrived with paramedics and a man was taken to hospital for further treatment.
His injuries are thought to be life-threatening and he is in a “critical condition”.
Blackheath Road is closed between Lewisham Road and Deptford Bridge for police enquiries.
A Metropolitan Police spokesperson said: “At around 11:22hrs on Monday, 29 December officers responded to reports of a collision involving a cyclist and a van on Blackheath Road, Greenwich.
“Police and the London Ambulance Service attended the scene, and a man in his 30s was taken to hospital. His injuries have been assessed as life-threatening and he remains in a critical condition.
“Road closures are in place while officers continue to make enquiries.
“Anyone with information is asked to contact police by calling 101 or online, quoting CAD 2139/29DEC.”
