Cliftonville officials urged the visitors to follow safety advice as thousands of Hoops fans are expected in the city for the game at Solitude.
It follows four consecutive nights of violence across Belfast, where sectarian tensions are running high.
Reds director David Begley said: "Belfast city centre is a very welcoming place but people are very sensitive about colours, not just this week," he said.
"As a result, it's probably best to avoid wearing colours into the city centre tomorrow.
Celtic FC also advised fans who are in west Belfast before the game to get taxis to the ground to ensure their safety, instead of walking through potentially dangerous sectarian flash points.
"I would say to all fans to make your way up to Cliftonville Road from the city centre," he added.
"There are lots of friendly pubs here and indeed our own bar, the Cliftonville Social Club. By doing that you can avoid difficulties.
He added: "It can be tricky as 100 yards in the wrong direction and you could be in the wrong place."
The warnings come after four nights of disorder following the controversial banning of an Orange Order march on the Twelfth of July.
The first leg of the UEFA Champions league qualifier was originally fixed for Glasgow, with the second in north Belfast. That would have given more time for any 12th of July troubles to calm down.
But Cliftonville asked for the dates to be reversed to secure a television deal and guarantee a maximum crowd.
When Celtic travelled to Solitude at the height of the Troubles in 1984, the friendly match turned into a riot. The game was abandoned 11 minutes from time, rubber bullets were fired by police and 25 people were taken to hospital.
However these days the friendship and cultural similarities between both clubs and their respective fans means there should be little animosity at the north Belfast ground, which has had its capacity increased to around 5,000.
'Anything can happen'
Meanwhile Celtic manager Neil Lennon has conceded that a shock defeat to the Northern Irish champions cannot be ruled out.
He said: "Anything can happen in football.
"It is a dangerous game and it is one we are not taking lightly. We will have to be at our best. I know it is early and I know some of the players won't be at their best but we will have to play very well to get a result tomorrow.
"Cliftonville will be highly motivated but the Champions League is so important to us as well.
"The difficulty is it comes so early. It is our first competitive game, we have only been back two and a half weeks and some players less than that, so it is a big ask but that is the reality."
Lennon said he does not want the night to become too friendly: "We have a great relationship with Cliftonville but once the whistle blows we will try to win the game.
"The atmosphere should be great, as long as it doesn't turn into a party-type atmosphere and the players get caught up with that.
"We are here to do a job and try to win the game or try to take some sort of result back to Glasgow next week."
Cliftonville v Celtic: Key battles
The Belfast Telegraph looks at the areas which could determine the outcome at Solitude.
MARC SMYTH v GEORGIOS SAMARAS
A defender with some pedigree, Smyth scored the winning penalty for Airdrie United in the 2008 Scottish Challenge Cup final against Ross County. The 30-year-old must call on all his experience if he is to have any chance of keeping Samaras quiet.
With a question mark hanging over Gary Hooper's future at the club, the onus will be on Samaras to come up with the goods in front of goal. The striker was on target during last year's qualifiers against HJK Helsinki and Helsingborg and will be hoping for a repeat this time.
BARRY JOHNSTON v KRIS COMMONS
Holding midfielder Johnston is in his third spell with Cliftonville and has scored in European qualification before. Similar exploits would be welcome against Celtic, but Johnston serves Cliftonville best by destroying the moves of the opposition.
Commons was one of Celtic's better performers last season and will be hoping to top those displays this term. The attacking midfielder weighed in with 19 goals but his ability to create opportunities for team-mates will be just as important as his own goal threat.
LIAM BOYCE v KELVIN WILSON
Last season's leading scorer in the Northern Irish top flight, Boyce returned to Solitude in January 2012 following a failed move to the Bundesliga with Werder Bremen. On home soil he was prolific once again, scoring 29 goals to seal the title last term.
With Efe Ambrose having had just one day's training and Charlie Mulgrew and Virgil van Dijk both injured, Wilson will be called upon to ensure the Hoops' defence is rock-solid. However, with 12 goals conceded in pre-season matches, an improvement will be needed in terms of the rearguard.
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