The discovery was made two days after the guest from Malaysia alerted the authorities.
The businesswoman told detectives that she had left the ring on a table on Friday while she went shopping in the city for a few hours.
On her return the ring was gone, she told hotel managers.
A day after she raised the alarm the hotel said it was still exploring all leads including the possibility of burglary.
Police scoured the hotel and prosecutors stood ready to take the case on if the disappearance had turned out to be the result of a theft.
“We’re talking about a colossal loss,” a source with the city’s public prosecutor told french newspaper Le Parisien.
However, the hunt was called off after the precious ring was discovered in a vacuum cleaner bag staff had used.
After the return of the hotel said: "We would like to thank the staff at the Ritz Paris who mobilised for this search and who work each day with integrity and professionalism."
It would not have been the first time that the luxury hotel in Place Vendôme had been hit.
A member of the Saudi royal family reported the theft of jewellery worth about €800,000 (£685,000) from her suite in 2018, and months earlier five armed men made off with jewels worth more than €4m (£3.5m) from display windows inside the hotel.