Since the outbreak began in April, more than 135,000 dengue cases and 650 deaths have been recorded in the world's eighth most populous country, the U.N. agency said.
More than 300 deaths from dengue were reported last month alone, WHO chief Tedros Adhanom Ghebreyesus told an online news conference.
"The outbreak is putting huge pressure on the health system," he said.
While cases were beginning to decline in the capital Dhaka, they were increasing in other parts of the country, he added.
The WHO said it has deployed experts on the ground in Bangladesh, and is supporting authorities to strengthen surveillance, boost laboratory capacity and increase communication with affected communities.
Dengue is a disease endemic to tropical areas that causes high fevers, headaches, nausea, vomiting, muscle pain and, in the most serious cases, bleeding that can lead to death.
The WHO has warned that dengue — and other diseases caused by mosquito-borne viruses such as chikungunya, yellow fever and Zika — are spreading faster and further due to climate change.
The agency's alert and response director Abdi Mahamud told the conference that such outbreaks were a "canary in the coal mine of the climate crisis."
He said that a combination of factors including climate change and this year's El Nino warming weather pattern had contributed to severe dengue outbreaks in several areas, including in Bangladesh and South America.
Countries in sub-Saharan Africa, such as Chad, have also recently reported outbreaks, he added.
Last week Guatemala declared a national health emergency for its own dengue outbreak.