The 28-year-old midfielder played in 133 games for the U.S. team, scoring 24 goals.
She also played professionally in the NWSL, winning a championship with FC Kansas City in 2015.
Lauren Holiday met Jrue at UCLA, where she played soccer and he played basketball.
Jrue Holiday, 26, has been with New Orleans the past three seasons, but has spent most of that stint injured.
He expects to return this season in full health, and the Pelicans see him as a core player along with All-Star forward Anthony Davis.
'The most important thing for Jrue to do right now is be with his wife and family,' Pelicans coach Alvin Gentry said in a statement.
'Every one of our coaches and players understands what Lauren and Jrue are going through, and they know we're behind them 100 per cent.
'We'll continue to do everything we can to support them and help them get through these hard times.'
In an interview with the Times-Picayune/NOLA.com, which first reported Lauren Holiday's condition and Jrue Holiday's plan to take leave, Jrue Holiday said Lauren was diagnosed with a benign, operable tumor on the right side of her brain.
The Pelicans have suggested that Holiday, whose salary is thought to be around $11million a year, will continue to be paid during his absence.
The team is planning to send a trainer to North Carolina to help him maintain his fitness and basketball skills during his absence.
Demps added: 'We encourage Jrue to take as much time as he needs to be with his wife and family before returning to the Pelicans.
'We understand that Jrue will miss some games, and his teammates are prepared to step up in his absence,' said Demps, whose own wife, Anita, is a cancer survivor and also has had a benign tumor removed from her brain.
'We will welcome Jrue back with open arms when he is ready to return to the team.'
Their baby is due in mid-October, and in the interest of the health of both mother and baby, Lauren's brain surgery will take place about six weeks after delivery, Holiday said.
The birth also could be induced early.
Jrue Holiday told the newspaper that Lauren has numbness on the right side of her face because the tumor is pressing on a nerve.
He said he and Lauren 'are still very excited about the birth of our first child, but our focus shifted from having this magnificent blessing to making sure everything is going to be OK with Lauren and the child.'
The couple has sought to guard their privacy during this time, and Lauren has yet to speak publicly about her condition.
For the time being, the couple plan to reside in Raleigh-Durham, North Carolina, near the Duke University medical specialists who will handle Lauren Holiday's surgery.
After her operation, Jrue will be a primary caretaker for both his wife and their daughter.
'My family comes before basketball,' Jrue told Nola.com.
'I'm obviously blessed to play this game and be in the position I am in, but my wife is the most important thing in the world to me. She comes before anything else.'
Last season, Jrue Holiday played in 65 games, averaging 16.8 points, six assists, three rebounds and 1.4 steals in 28.2 minutes per game.
For about the first half of last season, he played under minute restrictions as he came back from a stress fracture in his lower right leg that sidelined him for the better part of the previous two seasons.
His replacements to start the upcoming season could include Tim Frazier, who filled at the end of last season after Holiday was sidelined by fracture of his orbital eye wall.
New Orleans also acquired former New York Knicks point guard Langston Galloway this offseason.
Pelicans combo guard Tyreke Evans also has played point guard in stints throughout his career, but the timeline on his comeback from knee surgery remains unclear.
In the meantime, Jrue Holiday said his wife remains strong.
'Lauren has her good days and her bad days; some are better than others,' he told Nola.com.
'She's obviously a fighter, the toughest woman I know. That's the reason why I married her.'
