Zimbabwe says nearly 600 people have already died from the disease but aid agencies fear the toll could be higher.
Monasch told the BBC that aid agencies were doing everything possible to bring down mortality rates, but warned that he believed infection rates would rise sharply in next few weeks.
He said he was particularly concerned about the plight of children.
"Children in Zimbabwe are on the brink, and everyone's focus must now be on their survival," he said.
UNICEF has launched an emergency response programme in Zimbabwe to focus on providing basic services for children, including providing nutritional supplements, and trying to increase access to safe water in the short term.
Zimbabwean state media on Sunday blamed the cholera outbreak on European sanctions imposed on the regime of President Robert Mugabe.