Pique, who is regularly booed by large sections of Spain supporters for his outspoken comments against Real Madrid and his perceived support of Catalan independence, tweeted in favour of Sunday's referendum on Thursday - without backing a split for Spain - but urged supporters to behave peacefully.
Ramos later criticised his team mate for wading into the debate on the referendum, which the Spanish government deems illegal and has tried to prevent from taking place, as tension builds in the country ahead of one of the most significant days in the 39 years since Spain returned to democracy.
"Pique's tweet was not the best thing to do if he doesn't want to be booed," Ramos told reporters.
Ramos and Pique, in being flag-bearers for fierce rivals Real Madrid and Barcelona, have long had a delicate relationship as Spain's two main centre-backs but have generally managed to patch up their differences when playing for the national team.
Ramos, however, said Pique had risked causing divisions in the Spain camp with his comments.
"Perhaps the tweet is not the best thing for the group," he said.
"Everyone is free to say what they think, although as a captain I'm always concerned about the atmosphere in the team and Pique knew what he was doing. Maybe it wasn't the right time to do that and it doesn't help a lot."
Spain begin preparations for their final two World Cup qualifiers next week, hosting Albania on Friday and visiting Israel on Monday.
They need four points from the two games to book their place in Russia.