The 22-year-old Wales international was knocked out during Friday's 52-30 Premiership win over Wasps.
It was North's fourth head injury in the last five months and he is now seeking advice from a neurosurgeon.
"We won't play him at the weekend. Clearly he had a nasty knock," Saints coach Jim Mallinder said.
"He's making good progress. The day after he was up and about.
"He's improving and down there at the moment going to see a neurologist. We'll wait to see what the experts say."
Wasps forward Nathan Hughes has been banned for three weeks for the incident that led to North being knocked unconscious.
Hughes was found guilty by an RFU disciplinary panel of "striking with the knee and/or shin".
North missed Wales' 12-6 win over South Africa in the autumn internationals after being concussed against New Zealand, and was then struck twice on the head while playing against England during the Six Nations.
Former World Rugby medical adviser Dr Barry O'Driscoll said on Monday that North should not play again this season.
When asked if North's season could be at risk because of the injury, Mallinder replied: "I think you have just got to be careful not to get too carried away.
"There are a lot of so-called experts out there giving amounts of weeks and months that players should be out.
"You need to look at every single player individually, you have got to know what their medical record is and what has happened in the past.
"That's what the specialist knows. He has got all that detail, and he'll make his specialist opinion, and we will be fully guided by that."
Northampton wing George North will miss Saturday's European Rugby Champions Cup quarter-final with Clermont Auvergne because of a head injury.