Police hunting for the gang said the driver of the van was attacked by at least two men in a secure area at the airport's Terminal 4 at about 6.30am.
The robbers forced him to the ground and bound his wrists before transferring the cash into another British Airways van. The second van was later found abandoned and burned.
The cash - used banknotes destined to go back into circulation in the UK - arrived on a flight from Bahrain and was being transferred to a holding cargo area at Heathrow.
The guard suffered shock and wrist injuries, which were not believed to be serious. Police said the guard had not reported seeing firearms during the robbery.
A Scotland Yard spokeswoman said: "At this early stage of the inquiry we are trying to establish the exact circumstances of the robbery.
"There was no trace of the cash or the suspects. A substantial amount of cash was taken but we are not prepared to say how much," she said.
Police appealed for witnesses, but no descriptions of the robbers were being released.
