The arrests were made late Thursday night by members of the Mumbai criminal branch's cyber police station, according to an official.
The idea to fuse the Amar Jawan Jyoti flame at India Gate with the National War Memorial has been criticised by Congress leader Rahul Gandhi.
West Bengal Chief Minister Mamata Banerjee emailed Prime Minister Narendra Modi a second letter on the subject on Thursday, characterising the action as "against the... core foundation of India's Constitutional plan."