No litter bins will be emptied and the council urges the public not to use them.
All libraries, community hubs and council waste sites have also been closed.
However, telephone access to community hub services is still available on 0113 222 4444.
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All children's playgrounds were closed on Monday, but parks remain open for people to exercise once a day, keeping to social distancing measures.
The council shut down the services following Boris Johnson's announcement on new coronavirus restrictions.
People will now only be allowed out of their homes to buy essential supplies, to exercise once a day, for medical visits or to provide care or to help a vulnerable person, or to travel to and from work.
However employees should only go to work where it is absolutely necessary.
A message on the council's website said: "The council is reiterating the importance of following the instructions laid down by the Prime Minister in order to stop the spread of coronavirus.
"If you need to get in touch with our customer contact centre on 0113 222 4444 please be aware that lines will be very busy and we will help you as soon as we can."