DA Gauteng provincial leader John Moodey said on Sunday that the party will table the motion on May 15.
The party blamed Makhura for the 144 Life Esidimeni patients who had lost their lives.
"The ethical and moral accountability for 144 deaths and the suffering of thousands more lies squarely with Premier David Makhura. It cannot be business as usual for the premier who is ultimately responsible for a gross miscarriage of leadership by his provincial government," Moodey said.
Moodey said Makhura did not "care enough" to establish the facts of the Esidimeni saga.
In return, the ANC said the motion was a desperate attempt by the DA.
"The desperateness of the DA in Gauteng has reached crisis proportions as the party realises that their dream of unseating the ANC nationally remains but a dream, and now has naively set their eyes on Gauteng province," ANC Gauteng spokesperson Motalatale Modiba said.
Modiba said the party had been unsuccessful in tabling "endless motions of no confidence in Premier David Makhura".
"How does a party that is failing dismally to address the issue of diversity and race think it will successfully run such a diverse province as Gauteng is?"
Modiba said the latest motion was "nothing but a cheap attempt to exploit the deep wounds and pain suffered by affected families and patients following the Life Esidimeni tragedy".