It said it will unveil the measures in the next 24 to 48 hours.
The government also said it might use the military and the Nigeria Police for contact tracing.
It expressed worries that more than 1,300 contacts who have dissolved into the society and yet to be traced.
The government said with the likely multiplication of infections every five days, thousands would have been affected.
The Minister of Information and Culture, Alh. Lai Mohammed made the disclosures at a briefing in Abuja.
He said: “We should be ready for tougher measures. The forms they will take will be out from the end of today or tomorrow. But Nigerians should be ready for tougher measures.
“If we don’t do proper contact tracing, the figure will multiply every five days. Nigerians must take ownership of this initiative.
“We won’t hesitate to use whatever measure to ensure that you do not endanger other Nigerians. Containment is
very cheaper than cure.
A few people have helped. If you know you traveled recently, give yourself up to relevant agencies.
” If the situation warrants, we may be forced to use the police and the military for contact tracing. The police is already working on that. We don’t want the figure we have now to multiply. We should work towards containment which is cheaper.