A man has been shot dead there after he tried to seize a soldier's weapon.
The airport - the city's second largest - has been shut and flights in and out have been suspended.
In a tweet, South Wales Police said fans should "follow advice of local authorities, airport and your travel operators".
There are no direct flights from Cardiff, Manchester or Liverpool into Orly airport on Saturday.
However some flights to Paris' main airport, Charles De Gaulle, have been delayed as planes are diverted from Orly.
The Foreign and Commonwealth Office issued the following advice to travellers: "There are reports of an on-going police operation at Orly Airport in Paris.
"You should exercise caution, avoid the affected area and follow the advice of the local authorities.
"There will be reinforced security controls in place at the France v Wales Six Nations rugby match.
"If you're travelling to the match, arrive early at the Stade de France and follow the advice of the local authorities."
The Stade De France has advised fans to arrive early as increased security at the gates could cause delays.
Rugby fans in Paris for the Wales v France Six Nations match should "be aware" of the situation at Orly airport, South Wales Police has said.