The West has sent proposals to calm the crisis in Ukraine via US Secretary of State John Kerry, Fabius told France Inter radio.
"If they respond positively, John Kerry will go to Moscow and then sanctions will not be immediate," he said. "If they do not respond or if they respond negatively, there will be a series of sanctions that could be taken as early as this week,"
On Monday Kerry refused to attend talks in Moscow after Russain Foreign Affairs Minister Sergei Lavrov snubbed Ukraine's interim leaders.
Lavrov declared that the proposals, whose details have not been made public, "do not suit us very much" and promised to present a Russian solution to the crisis.
The sanctions could include "freezing personal assets of Russians or Ukrainians and sanctions on travel, regarding visas", Fabius said.
Crimea's planned referendum on joining the Russian federation is illegitimate, he said.
"The only legitimate vote is the 25 May for the president of the Ukrainian republic, he added.