Can I Install Ceramic Tile Over Sheet Vinyl Flooring?

I wouldn't try the ceramic directly on the vinyl because I don't think it will create a good bond.
I would put down backer board (cement board, wonder board) which has a concrete type surface.  It comes in 1/4 inch and 1/2 inch.  It should be screwed down.
Make sure your floor has the right thickness as recommended by the ceramic tile manufacturer.  The backer board can be used to make up shy floor thickness.

Applying tile over vinyl flooring is a bad idea. Over the years, the vinyl will break down and cause the tiles to pop up.
You do not say what type of sub-floor you have, but if it is concrete, scrape off the vinyl, ( you can purchase a floor scraper from a local hardware store, such as Home Depot), then lay the tile directly over the concrete.
If you have a wooden subfloor, it should be at least 1/2 inch thick plywood, but 3/4 inch is the best way to go.
Apply a concrete leveling mix by spreading it over the plywood sub-floor. This serves three purposes. 1) It will level the floor out and 2), it will create a surface which will provide a good bond between the floor and the thinset mortar mix. 3) It will seal the subfloor.
If your sub-floor is wooden and not in good condition, it would be best to tear it up and replace with 3/4 " plywood.
If it is in good condition, but not thick enough, then I would do as freedom1st suggested and lay backer board or better still, (since it is going on the floor), would lay concrete board. It is sturdier.