"The EU is strong enough to withstand Britain's withdrawal," she told the German parliament ahead of a crisis summit of the 28 member states in Brussels.
"It is also strong enough to successfully defend its interests in the world in future."
Voicing confidence in the union as it confronts the first defection since its founding, Merkel said the EU would continue to be a guarantor of "peace, prosperity and stability".
Merkel, who is expected to take a leading role in future negotiations with London, again voiced her regret that Britain had voted in a referendum last week to quit the bloc.
She said both sides had a "strong interest" in maintaining "close and friendly relations".
But she stressed Britain would not be able to dictate the terms of its ties to the EU.
"We will ensure there are no negotiations based on the principle of cherry-picking," she said to applause.
"There must be and will be a noticeable difference between whether a country wants to be a member of the European Union family or not."
She added: "Anyone wishing to leave this family cannot expect to lose all the obligations but keep the privileges."
"This applies to Britain as it does to everyone else," she said.
A non-EU country can join the common market if it accepts the free movement of people, goods, services and capital, she added, mentioning the example of Norway.
Merkel, who had huddled with the leaders of France and Italy Monday in the aftermath of the shock referendum, said the three biggest economies on the continent had agreed on a "common position" on the approach to the Brexit vote.
After their talks in Berlin, the trio urged steps among the remaining 27 members to jointly boost cooperation on security as well as programmes to boost economic growth and youth employment.
Merkel said she hoped the Brussels summit would take place in that spirit of unity, and said the EU should aim to complete reforms of the bloc in time for the 60th anniversary of the Treaty of Rome laying its foundations in March 2017.
The German leader said she would welcome "any proposal that would lead the European Union of 27 (member states, without Britain) out of this crisis".
But she warned against moves that would strengthen the "centrifugal forces" threatening to tear the EU apart.
"I will act with all my strength, and so will the German government to prevent that," she said to more applause from the chamber, "and I see a good chance that we will succeed."