What are the minimum camera characteristics required to record a movie for cinema?
If I understood your question correctly, you want to project a movie on a cinema.

This would depend on the projector used by the movie theatre. Most movie theatres use film projectors, for which there really isn't a "quality", but rather you'd have to worry about getting a decent camera with decent film at the correct size. In this case I don't know much about transferring from digital to film. 

If the movie theatre uses a digital projector though, they usually come in 2K (2048×1080) at 24 or 48 frames per second, or 4K (4096×2160) at 24 fps if they follow the DCI specification. Basically, get the best camera you can get. 2K should be enough to have a pretty good quality experience at the distance a cinema projection is seen from.

Also remember though, the quality does not only depend on the amount of pixels on screen, but also on the compression used, and the sensor of the camera itself, so be prepared for large files or a lot of processing to compress your movie to a high quality profile.

If you can't get a 2K camera, 1080p should do: it's not too far from 2k: it the same vertical size, just a little less wide. 

Links that might help: 

http://www.mkpe.com/digital_cinema/faqs/tech_faqs.php#2K+4K
http://en.wikipedia.org/wiki/Digital_cinema

Hope it helps!