The object has been compared to an Imperial Cruiser in the Star Wars films and witnesses estimated it could be up to a mile wide.
Two film clips exist which appear to show the same object and footage has been repeatedly playing on Russian television news channels.
The shots, one taken at night from a car and one during the day, were both filmed by amateurs.
The 'craft' was said to have hovered for hours over Red Square in the Russian capital.
The clips of the 'invasion' have gone to the top of the country's version of YouTube.
The identity of the shape has not been confirmed. Russian reports ruled out a UFO but police refused to comment.
Nick Pope, a former Ministry of Defence UFO analyst, said it was "one of the most extraordinary UFO clips I've ever seen".
"At first I thought this was a reflection but it appears to move behind a power line, ruling out this theory."
A spokesman for aerospace journal Jane's News said: "We have no idea what it is."
