Bypolls to the Gurdaspur Lok Sabha seat and Kerala's Vengara assembly seat will be held on October 11 for which separate notifications will be issued on September 15.
September 27 will be the last date of filing nominations, the Commission said in a statement.
A BJP MP, Khanna had died of cancer on April 27 this year.
The Vengara bypoll was necessitated after sitting MLA P K Kunhalikutty of the UDF won the Malappuram Lok Sabha bypoll.