The Trust said both the LGI and St Jame's Hospital were currently "extremely busy" and offered alternatives for residents with minor injuries to attend.
Their post said: "The Emergency Departments at Leeds General Infirmary and St James’s Hospital are currently extremely busy.
"If you need care but it is not an emergency, please call NHS 111 or use https://111.nhs.uk/ and you will be directed to the most appropriate place.
"The NHS 111 team can also help you to make an appointment to attend urgent treatment centres and minor injuries units in Leeds.
"This includes the Shakespeare Medical Centre in Burmantofts, St George’s Urgent Treatment Centre in Middleton and Wharfedale Urgent Treatment Centre in Otley.
"The urgent treatment centres in Middleton and Otley can also carry out x-rays, urine tests. and provide prescriptions for minor illnesses."