Nørgaard joined Everton from Arsenal in the summer but is yet to make his debut for the club, kept out by a groin injury sustained soon after his arrival at Hill Dickinson Stadium.
Moyes admits the timescale has caught the club by surprise.
"I don't think we expected the injury to take this long when we signed him," said Moyes. "We look forward to getting his experience, but we haven't even had him on the grass yet.
"It's disappointing, but hopefully it won't take too long."
The Everton boss expects the 32-year-old to be available for selection once the September international break concludes in October, having already missed the club's opening four matches of the season across all competitions.
Nørgaard had spent one season at Arsenal, where he won the Premier League title after arriving from Brentford, the club where he made over 180 appearances and served as captain following his earlier move from Brøndby in Denmark.
The Denmark international brought his own international career to a close in the spring, retiring after 41 caps having missed out on qualification for the World Cup with his country.
His focus since has been entirely on club football, and the delayed start at Everton means Moyes has so far been unable to call on a player signed specifically to add experience and know-how to his midfield options.
The Toffees have had to manage a string of fitness issues in the same area of the pitch this season, with James Garner only recently returning to full training and further competition for places expected once Nørgaard is finally available to select.
Everton's next fixture arrives before the international break, with Moyes still assessing his options in the middle of the park in Nørgaard's continued absence.
The 32-year-old will be eager to make his mark quickly once fit, having joined on a two-year contract with the aim of adding an experienced head to a developing Everton midfield, and Moyes has stressed there is no fresh setback behind the delay.