It would be 'constitutionally inappropriate' and would set a 'disturbing precedent' for the government to trigger Article 50 to leave the UK without explicit parliamentary approval, the Committee said in a report.
While legally the referendum was advisory, "it was accompanied by a clear undertaking by the government, based on a manifesto commitment, to implement the decision reached in the referendum", the report said.
However, in the UK's representative democracy, it should be parliament that takes the decision to act, it said.
Parliament should therefore play a central role in the decision to trigger Article 50, and scrutinise both the Brexit negotiations and the final deal reached with the EU, it said.
It is unclear whether Article 50, once triggered, can be unilaterally reversed by the UK, the report said, so parliament should act on the assumption that it cannot. Article 50 should be triggered "only when it is in the UK's best interests to begin the formal two-year negotiation process", it said.
Lord Lang of Monkton, chairman of the committee, said: "The referendum result was clear and it is right that the government is preparing to take Britain out of the EU. However, our constitution is built on the principle of parliamentary sovereignty and the decision to act following the referendum should be taken by parliament."