England's Rugby Football Union rules state that only home-based players can be eligible for the national team.
Arundell signed a one-year contract with the Paris club in July following the bankruptcy of his previous team London Irish.
He was allowed to represent England at the World Cup, where they finished third after being knocked out in the semi-finals by South Africa, due to the 'special circumstances' rule, scoring a joint England record five tries on his tournament debut against Chile in September.
Under his new contract, however, Arundell will not be available for coach Steve Borthwick's squad.
"We are delighted to see Henry extend his contract with Racing 92. He only joined our squad a few weeks ago but has already demonstrated all his qualities as a great competitor and a great deal of maturity," Racing 92 chairman Laurent Travers said.
"He fits in perfectly with the club's short- and medium-term objectives, and we are convinced that he will be one of the driving forces behind achieving them."
Arundell has won 10 caps since making his senior England debut in July 2022.
The intention of the RFU rule, introduced in 2011, is to protect the quality of the English league by ensuring that the country's best players play in it.
