The Hoops will have to play three league games in between this Wednesday and next Tuesday plus their Scottish Cup semi-final with Aberdeen on April 17 before the final match of the season on the 20th.
But they also have to find time to play the Inverness match which at this stage looks like happening on Thursday the 14th.
Celtic chief executive Peter Lawwell has questioned the decision to postpone the weekend's clash at Caledonian Stadium on the morning of the game and was hoping the Scottish Football Association did the right thing by the fans with the scheduling of the re-arranged fixture.
"Inverness are a great community club and George Fraser (chairman], Graeme Bennett (director of football] and the rest of the board always make us and our supporters feel very welcome, so it is a difficult situation, but clearly there is something wrong with the drainage of the pitch here," Lawwell said.
"I have great sympathy for our supporters who were already on their way and we can only apologise to them. We value their support and they do need to be considered when it comes to setting kick-off times, otherwise they are going to end up saying 'enough is enough' if they're being asked to travel to games such as Inverness with a midday kick-off time.
"Our fans are the lifeblood of our club, and of Scottish football. Television is obviously an important income generator in Scottish football, but the fans need to be considered more in order that we can achieve a balance.
"This is the beginning of April and we're still getting games called off, and in top-flight Scottish football some overnight rain shouldn't cause a match to be called off."