"It's fantastic timing for us that it's the Women's World Cup," Chadha told the BBC.
"It's even greater news that the England team are doing so well.
"As soon as they get back to Heathrow that's the first thing we're going to do - invite them all, and maybe they'll take a bow themselves."
At the curtain call on Wednesday's opening night, at London's Phoenix Theatre, the cast unfurled a banner in support of the England women's squad.
"We got to hold the banner at the end with pride," said Natalie Dew, who plays the lead role of Jess, a Punjabi Sikh teenager forbidden to play football by her parents.
"We are so happy that they remain in the finals."
The England team's Casey Stoney was a consultant for musical's football choreography.
The show's gala opening was attended by actress Juliet Stevenson, who also appeared in the original film. "It's kept the heart and message of the film," she said.
Chadha's 2002 movie, which launched the careers of Keira Knightley and Parminder Nagra, was a huge hit at home and abroad.
The new musical version includes songs composed by Howard Goodall, with lyrics by Charles Hart.
Chadha, who grew up in London's Southall, said the story carried a "great message for girls".
"It's about a young woman who dreams of doing something that is seen to be very much part of a man's world, and how she earns the right to take on the world for herself despite everyone saying 'don't do it'.
"It's not just about football, but everything in life."
She said David Beckham's manager had said the football star was "desperate to come and see it with his family".
Chadha admitted that new musicals in the West End were a "risky business".
Made in Dagenham - also based on a British film - closed in April after a West End run of six months.
"All you can do is your best - tell your story with as much honesty and integrity as you can," she said.
"I really hope the British public come to see it, and appreciate it as a new kind of West End British musical, because that's what we were trying to achieve."
The musical begins with the voice of veteran football commentator John Motson, who was also in the audience on Wednesday night.
He said: "With our girls doing so well in the World Cup, it couldn't have been staged at a better time."
Bend It Like Beckham is booking at the Phoenix Theatre to 24 October 2015
