"As the government of Turkey, we will not be leading, we are not going to organise such events," Ali Babacan said.
"But on the other hand, if in some segments of the society, some civil actions, will do things in that line, it is up to our people," he told journalists in Brussels.
"It will definitely cause some backlash in Turkish society," he added. "Time will show."
Ankara had threatened economic reprisals against France if the bill becomes law, warning that French firms could be excluded from public tenders and a boycott of French goods might be imposed.
The draft law -- which has provoked the fury of Turkey, the modern state that emerged from the Ottoman Empire -- was adopted Thursday by the French lower house of parliament.
It now goes to the Senate, or upper house of parliament, for another vote.
Babacan said he thought the vote might be linked to next year's presidential elections in France but that he doubted the bill would make it into law.
"In times of elections, sometimes rationality could be delayed or put under the mattress for a while," he said.
"We would be very suprised if this bill continues at further steps."
Ankara contests the term "genocide" and strongly opposed the French bill.
It says 300,000 Armenians, and at least as many Turks, died in civil strife when Armenians took up arms for independence and sided with invading Russian troops as the Ottoman Empire fell apart during World War I.
Armenians say up to 1.5 million of their ancestors were slaughtered in orchestrated killings, which they maintain can only be seen as genocide.
