Prague has promised to tighten safety at Temelin
It is seeking to block Czech efforts to join the European Union unless the the Russian-designed station is closed.
The move has caused a rift within Austria's ruling coalition, with the centre-right Austrian People's Party opposing the initiative.
Chancellor Wolfgang Schuessel has urged members the People's Party not to sign the petition on the grounds that it could damage Austria internationally and isolate it within the EU.
Prague has promised to tighten safety at Temelin but says closure is out of the question. The plant is due to become fully operational next year.
While the result of the petition will not be binding, correspondents say strong support for it could put the coalition under strain, could even hasten its collapse.
Temelin has long been a cause for concern in Austria, where nuclear power was banned by a binding nationwide referendum in 1978.
'No capitulation'
The Freedom Party leader and Austrian Vice-Chancellor, Susanne Riess-Passer, told supporters on Sunday that success in the referendum was probably the "last chance" to get the plant closed.
She said her party would not "go down on our knees and capitulate to the nuclear lobby".
But Czech Foreign Minister Jan Kavan said that while the plant would not be closed the referendum could have very negative consequences for Austrian-Czech relations and Austria's position in Europe.
"I don't see one single reason for the Czech side to change its position on Temelin on the basis of the Austrian referendum," he told the Austrian weekly Profil.
Fierce criticism
Temelin was first planned by Czechoslovakia's communist authorities in the 1980s but its completion was thrown into doubt after the transition to democracy in 1989.
The Czech Government's decision finally to go ahead with the construction attracted fierce criticism from environmentalists and from Austria.
Czech and Austrian leaders resolved the dispute with an agreement to set up a joint safety commission for the plant. In return, Vienna promised not to block negotiations on Czech entry into the EU.
However, the plant has seen frequent shutdowns and safety scares.
Most recently - Reuters news agency reported - it was closed on Friday because of a problem in an electrical generator in the non-nuclear part of the station, after reaching 100% output for the first time.
Plant spokesman Milan Nebesar said the glitch, which was fixed the following day, never resulted in any threat to nuclear safety.