Mr Williamson, speaking at Defence Questions, said:
"This country always has and always will succeed, whether we're in the European Union, whether we're outside of the European Union, whether we have a deal or no deal, Britain will succeed and Britain will prosper."
He made the remark in response to a question from Shadow Defence Secretary Nia Griffith who raised concerns about the dangers of a no-deal Brexit for defence.
She said: "No deal means that we would have to withdraw from all CSDP (Common Security and Defence Policy) missions with our seconded personnel sent home forthwith, we'd be permanently shut out of the European Defence Agency and the defence fund undermining vital research in industrial cooperation and our defence industry would be hit by crippling tariffs and delays at the border putting in jeopardy the equipment that our armed forces need.
"So given all of this, does the Secretary of State agree that a no-deal Brexit would be catastrophic for defence and security?"
Mr Williamson responded: "I don't agree at all, our country can and will succeed with whatever it has to deal with and whatever it faces.
"Much of defence collaboration is done through third-party organisations, whether it's NATO, whether it be through the United Nations, whether it be joint expeditionary force and actually as I already touched upon most of our defence industrial collaboration is not done through the European Union."
A Labour MP claimed the Government's "botched" Brexit negotiations over the Galileo satellite system were risking lower investment in the Armed Forces.
Lyn Brown said: "£1.2 billion of UK investment in the Galileo system may now have been wasted because of this Government's failed negotiations. This Government now wants us to spend billions more on a delayed, diplomatically divisive and frankly sketchy system just to cover up for their failure.
"How much more does the minister expect the women and men of our Armed Forces to suffer from lower investment in them because of this Government's botched Brexit negotiations?"
Defence minister Stuart Andrew replied: "£92 million has been allocated from the Treasury EU exit fund to the engineering, development and design phase of a UK global navigation satellite system which is currently underway.
"The UK Space Agency is leading the work with the full support of the Ministry of Defence."
Shadow defence minister Wayne David asked how many British companies had "lost out on important contracts for Galileo as a result of the Government's failure".
Mr Andrew replied: "I'm sure that the great British industry that we have will provide us with a system that we need."