Drobny, who was on-loan at Villa in the 2004-05 season, was on holiday at the Spindleruv Mlyn resort in the northern Czech Republic when the accident occurred.
He was reported to have skidded off-piste into a tree at high speed on Friday morning.
The towering centre-back played twice for Czech Republic in 2004, after rising to prominence at French club Strasbourg.
He failed to make the first team at Villa and returned to his homeland with Sparta Prague, where he won the Czech League in 2007.
A Villa statement said: "Villa are saddened to hear of the sudden death of former player Vaclav Drobny ... Our thoughts are with his family at this very sad time."
Drobny also played for FC Augsburg in Germany, and was most recently at Bohemians Prague.