Ukraine was ordered to play a game behind closed doors as part of a UEFA punishment for racist behavior at last month's European Championship qualifier against Spain.
UEFA also fined Ukraine 97,000 euros for the racist behaviour and separate charges including offensive chanting and the use of a laser pointer.
On Wednesday, UEFA handed Ukrainian champion Dynamo Kiev a three-game stadium ban, with one game suspended, after racist attacks on black fans during a Champions League game against Chelsea.
Ukraine will already have to play its first 2018 World Cup qualifier behind closed doors because of a FIFA racism sanction dating from 2013, and it was given a partial stadium ban from UEFA last year.
Zavarov, who works under head coach Mykhaylo Fomenko, told the channel in a telephone interview that Shevchenko, 39, would bring new ideas into the team's coaching set up.
Shevchenko is Ukraine's record scorer with 48 goals in 111 games and won the Ballon d'Or in 2004 at AC Milan. He retired after Euro 2012 which Ukraine co-hosted with Poland.
Shevchenko was approached by the Football Federation of Ukraine to take over as head coach in November 2012 but declined because he did not have the required coaching qualifications.
That obstacle was removed in March 2015 when Shevchenko, who also played for Dynamo Kiev and Chelsea as well as Milan at club level, completed a two-year programme for a UEFA Pro Licence.