The US movie director told Russian state TV that he had received the first of two jabs of the Sputnik V vaccine.
The companies said in a statement that "insufficient response in older adults demonstrates the need to refine concentration of antigen in order to provide high-level response across all age groups."
Russia has started its COVID-19 vaccination programme, with the first jabs going to workers at high risk of becoming infected with coronavirus.
Brussels has made a festive warning and called on EU countries to remain vigilant against coronavirus until a vaccine is widely available.
Pfizer and BioNTech requested authorisation from the European Medicines Agency for emergency use of their coronavirus vaccine candidate.