The game was level at 0-0 when the players went off and will be replayed on Sunday.
“The #WCQ match between Croatia and Kosovo has been abandoned due to adverse weather conditions and postponed for Sunday 3 September,” FIFA said on Twitter.
The abandonment means that Croatia, temporarily at least, lose top spot in Group I of European qualifying.
Ukraine jumped up from fourth to first thanks to a 2-0 home win over Turkey as new Borussia Dortmund winger Andriy Yarmolenko scored a brace.
Iceland, who were second going into the day, saw their hopes of reaching Russia take a hit with a surprising 1-0 loss in Finland.