Solanke joined Spurs from Bournemouth on August 10th for an undisclosed fee, reported by British media to be around 65 million pounds ($85.40 million).
He picked up an ankle injury in their season-opening draw at promoted Leicester City and missed last week's 4-0 win over Everton.
Postecoglou said the striker was close to making his return but would not be rushed back against Newcastle. Richarlison is also out after suffering a muscle injury.
"Dom Solanke is close but I think we'll err on the side of caution with the international break," Postecoglou told reporters. "Richy pulled up sore. I think there's a muscle injury there and we're getting more information but he is out."
Midfielder Rodrigo Bentancur is available again after missing the Everton game due to concussion protocols, the manager added.
Spurs have had a busy transfer window, with Solanke the most high-profile of several arrivals. The club have also said goodbye to a host of players including Emerson Royal, Ivan Perisic, Eric Dier and Tanguy Ndombele.
Postecoglou confirmed that defender Sergio Reguilon and midfielder Giovani Lo Celso were seeking to leave ahead of Friday's transfer deadline, with Argentine Lo Celso linked in media reports with a move to Spanish side Real Betis.
"Both players are exploring options and I don't get too involved in that," the 59-year-old said.
"It's between them, their representatives and the club. I don't know what activity there is, but they're exploring options."
