The 88-year-old monarch, who is Canada's head of state, revealed that she was "shocked and saddened".
A single gunman, Michael Zehaf-Bibeau, opened fire at the national war memorial in Ottawa, Canada's capital, killing Canadian soldier Nathan Crillo.
Michael Zehaf-Bibeau later forced his way into the national parliament where he was killed.
On Wednesday evening the country's Prime Minister, Stephen Harper, read a statement from an undisclosed locaton.
"This week’s events are a grim reminder that Canada is not immune to the types of terrorist attacks we have seen elsewhere around the world.
"We are also reminded that attacks on our security personnel and our institutions of governance are by their very nature attacks on our country, on our values, on our society, on us Canadians as a free and democratic people who embrace human dignity for all."
He continued: "But let there be no misunderstanding. We will not be intimidated. Canada will never be intimidated."
On Thursday the national flag was flying at half-mast but parliament returned to work, with House speaker Andrew Scheer adding in a statement: "This sends a clear message of Canada’s resolve to maintain its free and democratic way of life."