Current fines issued to people who break coronavirus lockdown rules "aren't enough of a deterrent", according Dyfed-Powys's police and crime commissioner.
If people do not comply with the regulations, they can be directed to return home.
A number of fines can also be handed out.
Individuals who do not pay a fixed penalty notice under the Regulations could be taken to court, with magistrates able to impose unlimited fines.
If an individual continues to refuse to comply, they will be acting unlawfully, and the police may arrest them.
Individuals are only allowed to leave their home for the following very limited purposes:
Shopping for basic necessities and supplies, which should be as infrequently as possible;
One form of exercise a day - for example, a run, walk or cycle - alone or with members of their household;
Any medical need, to provide care or to help a vulnerable person; and
Travelling to and from work, but only where they cannot reasonably practicably work from home.
Dafydd Llywelyn told ITV Wales people are travelling "hundreds of miles" to the Dyfed Powys area.
It comes as people ignore repeated warnings not to travel over the Easter the weekend.
Community police officers were seen talking to people in a Cardiff park.
Holiday accommodation offered to key workers who cannot go home to their families has been vandalised, according to North Wales Police.
Vandals had painted the word "go home" on properties in Pwllheli, Gwynedd.
In a statement police said: "Ask yourself how you would feel returning to this after a long shift keeping the community safe.
Police forces across Wales took to social media on Saturday to say they've noticed the roads and beauty spots are quiet as people obey the lockdown rules.