Often outspoken, Pique has been targeted by boo boys during his time with the national team and Ramos pleaded with the Madrid supporters not to follow suit.
"To Pique or to anybody else you must always respect the players," Ramos told reporters.
"[I ask the fans] to support us, it will be a tense and difficult match.
"We want to perform well and play a good game."
Spain and Italy are level on 16 points atop the Group G standings, though Julen Lopetegui's men occupy the summit due to their superior goal difference after six matches.
Saturday's showdown in the capital will see the return of Spain's all-time leading goalscorer David Villa.
Villa – with 59 goals for his country and Euro 2008 and 2010 World Cup trophies to his name – was handed a shock recall at the age of 35, having not featured since the World Cup in 2014
The veteran forward has scored 19 goals for New York City in MLS this season.
"I think it surprised us all," Ramos said. "But it is well received.
"He still has a young spirit and always wants to score goals."