He was replaced as cabinet secretary by General Jose Amado Ricardo Guerra, a former top military official.
Lage had been credited with helping to save Cuba's economy by implementing economic reforms after aid from the Soviet Union ended in the early 1990s.
Perez Roque was once personal secretary to Fidel Castro, Raul's brother and the former president, and a former leader of the Communist Party's youth organisation.
Raul Castro, who took over the presidency in February last year from Fidel, had said for months that he would restructure the government to make it leaner and more responsive.
But Lucia Newman, Al Jazeera's Latin America editor, said: "This is an unprecedented shake up, as never before have so many government officials been replaced in one go."
"It is a new direction, we're just not clear what direction Castro is planning - a return to communist orthodoxy or pragmatism? However, Castro does seem to be trying to put in position people closer to him than to his brother, Fidel."
The ousting of Roque was a particular surprise to many analysts, as he was considered one of the most internationally prominent, and successful, members of Castro's government.
Our correspondent adds that the move could also be a message to the US, just a month before the summit of the Americas in Trinidad where the US could be pressured over its Cuba policies, that Cuba is aiming for change.
Jose Luis Rodriguez, the economy minister, Raul de la Nuez, the minister of foreign trade, and Jose Luis Gacia, the minister of economy and planning, were also removed from their posts.
Georgina Barreiro Fajardo, the finance minister, and Alfredo Morales Cartaya, the labour minister, were also fired.
The ministries of fishing and food were also combined as part of the changes, as were the ministries of foreign investment and foreign trade.
The changes were announced by state television on Monday.