"No, I don't think so," Riester told the BFMTV broadcaster, when asked whether the cathedral would remain closed within five years.
Riester did not say exactly when Notre Dame could reopen for visitors.
A massive fire broke out at Notre Dame late on Monday evening, causing the collapse of the cathedral's spire and two-thirds of its roof. The blaze was fully extinguished only on Tuesday morning.
Macron has described the incident as a "terrible tragedy."