The Chelsea captain was banned for four games and fined 220,000 pounds ($321,500) after being found guilty by the Football Association of racially abusing QPR defender Anton Ferdinand during a Premier League game in 2011.
Terry was later cleared following a criminal trial.
QPR fans are expected to vent their feelings at Terry again on Sunday, when Ramsey's side will be hoping for a victory to ease their relegation fears and leaders Chelsea will aim to take another step towards the Premier League title.
"Ultimately, John Terry is a player of Chelsea and I am the manager of QPR, and as a man and a person I would shake John's hand after the game," Ramsey, one of six managers from black and minority ethnic backgrounds in the English professional leagues, told a news conference on Friday.
"I don't know what his feelings are towards me. But as long as there wasn't anything unprofessional on the field by him, I would shake his hand.
"It was an episode for British society that sat uncomfortably, and it's not something you want to highlight in football. But it's been dealt with and we have to move on."
Ramsey said the reaction of QPR fans towards Terry was understandable.
"Fans are fans and it would be odd to think there wouldn't be extra feelings towards that situation," he said.
It was thought Terry might come face-to-face on Sunday with his former England team mate and QPR defender Rio Ferdinand - Anton's brother -- but Ramsey confirmed that Ferdinand will be out with an ankle injury.
Chelsea are seven points ahead of second-placed Arsenal and clear favourites to clinch their fourth league crown in 11 seasons, and Ramsey accepted that Sunday's game carried more significance for QPR.
Ramsey's side are third from bottom, two points from safety, with six games remaining. They have lost their last five home league games.
"Chelsea can afford to have a blip and still win the league," Ramsey said. "We need to pick up every point we can. We are expecting a tough game but the players will be up for it."
(Writing by Stephen Wood, editing by Ed Osmond)
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