The theatre had been due to host shows today (Saturday), but announced their decision that the performances would not take place just before 2pm.
Anyone who had a ticket will now be refunded.
A statement from the theatre said: "Given the situation in Ukraine, Royal & Derngate have taken the decision to cancel today’s performances of The Russian State Ballet.
"All customers who have purchased tickets for the ballet will receive a full refund and be contacted by the venue’s box office team over the next 10 days.
"They ask that you do not contact them at this time.
"We apologise for any inconvenience this causes and for this short notice in this announcement."
The announcement comes as Russian troops continue their invasion of Ukraine, which is braced for another night of assaults.
Ukraine's health minister announced earlier today that 198 of their citizens had died so far.
It's estimated 120,000 people have fled the country in the past 48 hours, with many others taking shelter in underground stations.