They said President Mahinda Rajapakse was "foolish" to become associated with Than Shwe, set to arrive on Thursday.
"The Sri Lankan government has been criticised for their human rights violations and restrictions on media freedoms," the monks said in statement referring to the conflict against Tamil separatists that ended in May.
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"We dare say the situation in Sri Lanka is several times better than in Myanmar," they added.
Than Shwe is to fly to the central district of Kandy on Thursday for a two-day tour of Buddhist temples and meetings with senior Sri Lankan officials, including talks with Rajapakse.
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The junta leader, who has not been to Sri Lanka before, is due to leave on Sunday after receiving blessings from Buddhist monks at a temple outside the capital Colombo.
Rajapakse visited Myanmar in June