North Wales Police are urging people not to travel to see the goats in Llandudno as this "is not essential travel."
The goats rose to national fame on Tuesday after videos of them running amuck around the town appeared on social media.
Lockdown rules mean people are only allowed to leave the home for essential reasons.
The goats normally live on the Great Orme but began exploring further into the town centre because the streets are so quiet during the coronavirus lockdown.
Since the stay-at-home rules came into place, police forces across Wales have been challenging those in breach of them.
North Wales Police took to social media to emphasise how visiting the Kasmiri goats was not classed as "essential" travel.
The also emphasised how travelling unnecessarily can put a strain on public services.
On Monday 30, South Wales Police urged MP Stephen Kinnock to comply with the lockdown rules after the politician posted a picture on Twitter of himself visiting his dad.
Mr Kinnock was there to celebrate his dad's birthday which the police said was not essential travel. The MP did clarify that he was also delivering "some necessary supplies" to his parents.
Last week saw the introduction of new police powers, giving them the authority to fine - or even arrest - those who ignore the stay-at-home rules.
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