Shevchenko, the country's record goalscorer with 48 goals in 111 appearances, was last week handed the opportunity to succeed Oleg Blokhin in the role following Blokhin's decision to join Dynamo Kiev.
"Representing the national team for many years was a great honour for me and with the team I enjoyed many memorable moments and vivid emotions," he said in a statement posted on the Ukraine Football Federation (FFU) website.
"I am grateful to the Federation for the high level of confidence they placed in me by offering me the chance to lead the national team.
"But I think today, to lead a team like Ukraine is a somewhat premature step for me.
"I hope the leadership of the FFU will react with understanding to my decision.
"I am confident the national team can get to the finals of the 2014 World Cup and, for my part, I am always ready to support our team to help get maximum results."