In a notice on Wednesday, the CS said: "Employers should allow Muslims to be away from work but for non-Muslims, this will be a normal working day."
Muslims worldwide will mark Idd ul Adha, also known as the "Sacrifice Feast", the second of two Muslim holidays celebrated each year.
Following the announcement, Kenyans on Twitter have accused the government of discriminating against non-Muslims.
Others asked whether Muslims will work on Christmas Day which is marked by Christians globally.
The anger was deepened after neighbouring Uganda asked its workers to stay at home on Friday.
Public Service PS Catherine Bitarakwate made the announcement in an August 25 notice.
"Idd ul Adha shall be observed as a public holiday throughout Uganda," she said.
Geoffrey Nyambane, a twitter user, asked: "One government, one holiday; a public holiday for all one year, only for Muslims the next year. Really?"
'@Nickmug said': "Is it constitutional? Doesn't it amount to discrimination?."
"This is religious discrimination, ni venye court wako busy otherwise ningepeleka petition (I would have petitioned if the courts weren't busy)," '@tony_werrason' said.
Supreme Court judges are preparing to make a ruling on a presidential petition by NASA principal Raila Odinga againt Uhuru Kenyatta's election victory.
Mwamuye Brian said: "This is the root of discrimination. What about Christmas and Easter holidays?"
Ng'eno Kobur wrote: "You should know that celebrating religious holidays builds religious tolerance. [Uhuru] please intervene."
Allan Gohole asked: "So will Muslims work on Christmas?"
-The Star| MERCY WAIRIMU