The 27-year-old was forced out of his country's 30-22 defeat to the All Blacks after 52 minutes following a hugely-committed tackle on Richie McCaw.
Hartley was discharged from hospital and then assessed by the England medical team and is now in the care of his club side, with more assessments planned before any further announcement is made.
"Dylan has been discharged into the care of Northampton. He will require a few days' rest and will be re-assessed by his club's medical team next week," read a Rugby Football Union statement.
Hartley was in fine form on his 50th Test cap against the World Champions at Twickenham and Northampton will be desperate not to lose him when they return to Aviva Premiership action this weekend.
After one round of Premiership fixtures and two weeks of LV=Cup games without their club captain in their ranks, the Saints welcome Newcastle Falcons to Franklin's Gardens this Saturday, before travelling to Worcester a week later.
Then comes the December double header with Leinster in the Heineken Cup, games that will decide whether their European dream will remain alive going into rounds four and five in the New Year. The first of those huge fixtures takes place in the East Midlands on Saturday, December 7 and the return clash in Dublin is scheduled for exactly a week later at the RDS.
Northampton currently sit second in Pool 1, three points behind leaders Leinster after a narrow loss at Castres Olympique and a home win over the Ospreys last month.