An independent regulator imposed the fine after Chelsea admitted to the charge, the FA said in a statement.
Chelsea were charged earlier this month after the bottle, which media reports said contained water, was thrown while Villa were celebrating their win on 27 December.
"I was made aware of an allegation that an unidentified member of the Chelsea technical area had thrown a plastic drinks bottle in the direction of the Aston Villa technical area," referee Stuart Atwell had written in his report about the incident.
Sixth-placed Chelsea visit Crystal Palace on Sunday as third-placed Villa play at Newcastle United.