The EC, however, did not give a date for holding the elections in its order issued on Friday.
"The tenure of 5 MLCs from graduates' constituency and 6 MLCs from teachers' constituency is coming to an end on May 6. Hence, elections should be held on these seats," Chief Electoral Officer of Uttar Pradesh Ajay Kumar Shukla said in a statement.
To conduct elections on these seats, at least four weeks' time is needed, he said.
"However, in wake of implementation of a three-week nationwide lockdown, the Election Commission of India has ordered that the process of elections to 11 seats of Uttar Pradesh Legislative Council shall be initiated at a later date after reviewing the situation," he added.
A graduates' constituency is one in which only graduates from any recognised Indian university, or those with an equivalent qualification, can vote.
In a teachers' constituency, only a full-time teacher in at least a secondary school or higher is eligible to vote.
The Uttar Pradesh Legislative Council has 100 seats. At present, it has a strength of 99, while one seat is vacant.
The lockdown, which came into force on March 25, was imposed by the Centre to control the spread of coronavirus in the country. NAV DIVDIV