Councillor Denise Jeffery said the council would close country parks across the district if they believed people were flouting the government's social distancing advice.
It comes just a day after West Yorkshire Police criticised a crowd of people who had gathered to take advantage of an ice cream van at Pugneys Country Park.
Coun Jeffery said: “We are now in a situation that we have never before experienced.
“Earlier this week the Government announced strict new measures to slow the spread of the coronavirus and reduce the pressure on the NHS and to save lives. We absolutely have to support these new restrictions.
“Our normal behaviour simply cannot continue. I understand that it can be hard to accept, but we must. The lives of everyone in this district rely on us following the stay at home and social distancing measures. Please do not underestimate the dreadful impact of ignoring them.”
Under the current government advice, people should stay home at all times, unless they are making trips for essential food or absolutely cannot work from home.
Going outside to exercise is permitted, but people should stay at least 2 metres away from others at all times, and should only visit parks or public spaces if they are within walking distance. In line with this guidance, Wakefield Council closed all play areas, but has so far kept parks and country parks open.
However, the authority have said they will closely monitor country parks over the next 48 hours, and, if necessary, will "close or restrict access to some or all of these sites as required".
Andrew Balchin, Acting Chief Executive of Wakefield Council, said: “The Government’s new restrictions currently encourage us to keep parks open, but we are asking residents to use these responsibly and strictly in line with Government imposed social distancing advice. This is for the good of everyone’s health and controlling the pandemic.
“We urge everyone to be responsible, do not take un-necessary journeys and follow the Government’s clear advice to stay at home, protect the NHS and save lives.”