Aberdeen and Celtic cancel parades after terror attack
There will also now be no cup presentation at Parkhead if Celtic win Scottish Cup.
Celtic have cancelled a bus parade planned for the weekend due to a heightened security risk after Monday's terror attack in Manchester.
The club have also informed fans there will be no trophy presentation at Celtic Park if they win the Scottish Cup on Saturday.
The Heroes and Legends bus parade due to take place before Sunday's Henrik vs Lubo charity match has been cancelled after discussions between Celtic and Police Scotland.
There will also be stronger security measures at the sell-out Celebrate 67 event at the Hydro on Thursday evening, which will be headlined by Rod Stewart.
Celtic have advised fans attending the event to arrive as early as possible to allow extra time for additional security checks.
They also confirmed full bag and pat down searches will be carried out and any bags larger than A3 size (35cmx40cm) will not be permitted into the venue.
In Thursday's statement released through the club's website, Celtic said: "Clearly, with absolute respect to Aberdeen Football Club, we would not wish to pre-judge the outcome of the Scottish Cup final in any way.
"However, it is very important that supporters are fully aware of all organisational arrangements which may affect them.
"In the event of Celtic being fortunate enough to win the Scottish Cup, the club would like to confirm that the team would not be able to 'present' the trophy to supporters back at Celtic Park and there would be no supporters' event there."
It added: "It is also important that supporters know that the planned Heroes and Legends bus parade, which was to be staged in advance of this Sunday's Celtic FC Foundation match at Celtic Park, has also been cancelled.
"Given the situation and the pressure on police and security resources, we are sure that our supporters will fully understand these measures which have been taken.
"We thank all our fans for their assistance and cooperation."
Aberdeen have also confirmed they will not hold a victory parade or celebrations at Pittodrie if they win the cup on Saturday.
In a statement, they said: "Following this week's tragic events in Manchester, and after detailed discussion with Police Scotland, Aberdeen Football Club has confirmed that, in the event of an Aberdeen victory, there will be no victory parade in the city on Sunday."
In relation to the heightened security, Police Scotland chief constable Phil Gormley said the force has "well rehearsed plans" to deal with any major incident.
He said: "We are reviewing all significant events along with event organisers taking place within the next 14 days and will increase the security footprint around those events where it is deemed appropriate.
"We have well rehearsed plans to respond to major incidents and we will be continuing to work with our partners to address the current heightened threat.
"However, there is no intelligence to suggest there is any specific threat to Scotland but I would ask the public to remain alert and report anything suspicious."