Ryanair lodged the claim under the provision of section 93 of the British Transport Act 2000, which it said reflected losses from cancellations and lost bookings over the week of August 10 to 16, the airline said on Friday.
Ryanair said it would donate any compensation received to charity.
"Ryanair's sole motive in this action is to defeat terrorism by returning airport security to normal, and since we don't wish to be seen to profit in any way from suing the government, all proceeds received will be donated to Orbis," Michael O'Leary, Ryanair's chief executive said.
However, the UK Department for Transport said Ryanair had no legal grounds to seek compensation. Other airlines said they had no plans to seek damages from the government.
Hand luggage restrictions and heightened security screening were introduced at airports by the government this month following what it said was a bomb plot.
"We continue to face a serious security threat and we are not going to compromise security," a transport department spokesman said.
"Aviation security measures are directed under the Aviation Security Act 1982 which does not have any provisions for compensation."
Last week, Ryanair approached British Airways, Virgin Atlantic and other airlines, urging them to sue the government for compensation.
A BA spokeswoman said on Friday that the airline did not plan to sue the government.