Judge John Guthmann did not say when he would rule on whether the disputed system can remain in place.
The Associated Press reports the judge said "the most I can do is stop the registration going forward," and that it would probably take a separate case to challenge the thousands of online registrations since the system launched in September.
Ritchie said earlier this month that he wants the lawsuit dismissed, claiming the plaintiffs are seeking an extraordinary remedy and can’t prove they’ve been injured.
Politics in Minnesota said the American Civil Liberties Union has also filed a brief in the lawsuit.
According to the blog, the ACLU isn't entirely siding with Ritchie, but argues the judge in the case cannot rule to invalidate the registrations of voters in the state who have already used the online registration system.
As of the first week of December, 2,225 people across the state used the system to submit voter applications or updated existing ones, the AP said.