The June 10 game will be hosted in Sfax in neighbouring Tunisia.
Tunisia has not allowed spectators to watch all but a handful of matches since the uprising in the country in January last year, which heralded the start of the Arab Spring.
Controlled numbers of supporters have been allowed to attend games in African competitions but league matches are all played behind closed doors because officials fear violence in the stands.
There has been no organised football in Libya since March 2011, when the uprising against Muammar Gaddafi's regime began.
Libya played two of their 2012 African Nations Cup qualifiers at neutral venues in Egypt and Mali but despite losing home advantage and having their team ravaged by the strife, they reached the finals, which were held in Equatorial Guinea and Gabon in January.
Libya's last home match was in October 2010 when they beat Zambia.
They begin their 2014 World Cup qualifying campaign with an away game against Togo on June 3.