The Election Commission says the statues might influence voters and must stay covered until the end of assembly polls in March.
Ms Mayawati is famous for building statues of herself and other icons of her low-caste Dalit community.
There are nearly a dozen statues of Mayawati in two parks in the state.
The parks in the state capital, Lucknow, and Noida, a suburb of Delhi, have more than 75 stone elephants.
The government has been ordered to cover the statues by Wednesday evening.
Under election rules, portraits and calendars bearing photographs of the chief minister must be removed from government offices ahead of elections.
More than 75 stone elephants have been installed in two parks
Chief Election Commissioner SY Quraishi said the covering up should be completed “at the earliest”.
Ms Mayawati’s Bahujan Samaj Party has termed the order as “one-sided and against natural justice”.