The game was tied at 1-1 when referee Craig Napier called a halt to proceedings in the 63rd minute due to fog descending on Rugby Park.
Wright was appointed by Kilmarnock in February but was unable to save the Ayrshire club from relegation to the Scottish Championship last season.
He leaves the side fifth in the table, five points behind league leaders Arbroath, having lost four of his last five league fixtures prior to the Dunfermline abandonment.
Confirming Wright had been relieved of his duties, Kilmarnock director Billy Bowie stated: “It is with regret that we have had to take this decision as I know how much Tommy wanted to bring success to Kilmarnock.
"We thank him for his hard work and dedication during his time at Rugby Park and wish him all the best for the future.
"Everyone at the club is under no illusions that promotion back to the Premiership is the nunber one target for the season and with half of our league matches remaining as well as the upcoming January transfer window our full focus is on appointing a new manager to achieve this goal.”