In response to MEPs' questions in Brussels on Tuesday, the minister said it should not become a precedent.
"I still believe that a democratically elected government cannot be removed by military force," Linkevičius told members of the European Parliament's Foreign Affairs Committee.
"You can like it, you can dislike it, but it is my position that I would like to share with you. It's not the fact we should be proud of, try to explain or legitimize or set as a precedent," he added.
Egypt's President Mohamed Morsi was removed from office by the country's army last Wednesday following a 48-hour ultimatum issued in response to massive demonstrations. The army commander said that the president was incapable of dealing with the deepening political crisis in the country.
Egypt's new leader Adly Mansour has pledged to hold new elections early next year.
Around 50 people were killed in a wave of violence on the streets of Cairo on Monday, with Islamist demonstrators blaming the army. Meanwhile, the interim government says people were killed when protesters tried to storm into the base of the country's Republican Guard.
