In a statement the Forum said that although the company is made up of many different nationalities with many from Ukraine, "the safety and consideration of our customers is our main priority".
A spokesperson said: "Both the Board and Staff at the Millennium Forum regret the impact this decision will have on the dancers/crew and promoter of Royal Moscow Ballet who have all been great friends of the Forum for many years now.
"Our thoughts and prayers are with the people of Ukraine at this terrible time.
"We would appreciate your patience as we contact all patrons to arrange for refunds as soon as possible."
The Royal Moscow Ballet has also issued a statement which has been shared by the Millennium Forum theatre in Derry.
It reads: "To whom it may concern. The Royal Moscow Ballet is a multi-national touring Ballet company who have been coming to Ireland annually for over 10 years now and always look forward to their annual tour of Ireland.
"The company is – and has always been – made up of different nationalities and on the 2022 tour we have Russian Nationals, Ukrainians, Belarussians, Uzbekistan Nationals, Japanese, Irish and Polish cast and crew, who have travelled, worked and lived together for years.
"They are young artistes who just want to perform the art form they love and have done since childhood; they bear no political leanings whatsoever and remain united as a group and as friends and wish only to spread the joy of their art form and culture throughout Ireland as they have done for the last 10 years.
"We hope this helps to clarify the diversity of our ballet company and that we don’t carry any political message on this tour."