Pique has been an outspoken advocate of Catalan independence from Spain, leading to fans of the national team abusing the Barcelona centre-back during a training session on Monday night.
Pique and Ramos, who have won 236 Spain caps between them, have frequently clashed in the past due to their El Clasico rivalry, and reports now suggest that their relationship is "broken".
Ramos appeared to criticise a tweet from Pique earlier this week which urged Catalans to "express ourselves peacefully" after protesters were shot with rubber bullets by Spanish police over the weekend.
"Pique's tweet was not the best thing to do if he doesn't want to be booed," Ramos told reporters.
"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 host Albania in their penultimate World Cup qualifier on Friday.