"But even if women aren't hurt, I'd like such expectations to be considered power harassment."
Ishikawa said Nemoto's remarks might prompt some women to bring the issue up with their bosses.
"This might spur that kind of action, so I think this is going in a good direction," she told Reuters.
The Health Ministry said it was reviewing the petition and declined to comment further.
Nemoto's comments have been broadly ridiculed.
"To say something like that is just beneath contempt," said Noriko Hama, a professor of economics at Kyoto's Doshisha University. "It's ridiculous that women should be told they have to wear high heels by a man."
"It once again reveals the mentality behind Japan's politicians," she said.
"The more they talk, the more they reveal their lack of intelligence — but, unfortunately, these attitudes are rooted among our leaders."
Kanako Hosomura, who worked as a waitress in Tokyo, recalls being told by a male manager that she had to wear heels throughout her eight-hour shifts.
"I could not believe what I was hearing," she said. "He was standing in comfortable flat shoes, telling me I had to wear heels. I was furious."
The response to the minister's comments online has been swift and unflattering. Some suggested that the minister should be required to wear high heels for a week to see if he enjoyed the experience.