"We're going to err on the right side," he said. "If they give me an option of 'you can play him every third game or give him two weeks rest,' I can tell you right now, I'm going to say 'two weeks rest' ... because at the end of the day, I want him right. I don't want him half right."
Guard Courtney Lee, who missed the game against the Grizzlies with a sprained left ankle, might return on Tuesday night, Rivers said.
Lee and Garnett both missed practice Monday.
The health problems are the latest in a string of injuries that already have sidelined guards Rajon Rondo and Leandro Barbosa and forward Jared Sullinger for the season. Barbosa was traded to the Washington Wizards after being hurt.
"Kevin went down and Courtney Lee going down, sometimes it kind of wears on you mentally because that's pretty much how the season has gone for us," Paul Pierce said. "Some way, somehow we've got to pick ourselves back up. It's been kind of devastating with the injuries so far, but we've got to find a way to persevere and fight through it."
Tuesday's game could be a preview of a first-round playoff series, and Pierce thinks beating the Knicks on Tuesday or Sunday -- or both -- could send a message.
"You get a chance to beat them a couple of more times, it really takes away a team's confidence going into the playoffs and so that's got to be a little extra motivation," Pierce said. "They've been playing well all year long. They're on top of the Atlantic Division. But right now it's about heading to the playoffs, picking up the pace."
The Knicks (42-26) have won their last four games after losing four in a row. The Celtics (36-33) have dropped their last four, matching their second longest losing streak of the season. Boston has struggled on defense and Garnett's absence won't help. In three of the last four games, opponents have shot better than 43.9 percent, the Celtics' field-goal defense for the season.
Rivers knew that Garnett's absence vs. Memphis was going to be a problem, especially since it was Boston's second game in as many nights.
"Back-to-back (games), no Kevin, no Courtney, a lot of new guys that were going to play," he said. "As a coach, you're just trying to find a way to win."
Now the Celtics have had two days without a game, resting on Sunday and practicing on Monday, as they head into a stretch of five games in seven days.
"We just haven't played well lately," Rivers said. "We just have to get it back and having all these guys in and out doesn't help, obviously. But everyone goes through it. New York went through it out on the road where they had all the injuries and then they kind of gathered themselves and now they're winning again even though they still have injuries.
"I think we're going to have to go through that same thing right now."