Fabio Capello's men qualified for the finals, which start next month, with little difficulty as they topped UEFA Group F after losing just two games during the campaign.
Russia were eliminated in the group stages in 1994 and 2002, but have a great chance to progress to the last 16 for the first time after being drawn in a wide open group.
The Russians will be in Group H alongside Belgium, South Korea and Algeria in Brazil.
Capello's side are second favourites to win the group behind a talented Belgium side, and the Italian will be keen for Russia to build momentum ahead of their opening clash with South Korea on June 17.
Russia will be expected to gain a morale-boosting win against a Slovakia side already looking ahead to the qualifying campaign for the 2016 UEFA European Championship in France.
Slovakia finished third in Group G in qualification for the World Cup, but never looked like reaching the finals as they finished 12 points behind the top two of Bosnia-Herzegovina and Greece.
Jan Kozak's men are likely to have a better chance to qualify for Euro 2016, which will feature 24 teams, but face a daunting group that contains Spain, Ukraine and Belarus.
Slovakia started their build-up to that campaign with a 2-0 win against Montenegro on Friday.
History suggests that this game will be a tight encounter, with the seven internationals between the two since the break-up of Czechoslovakia in 1993 all settled by a goal or ending in a draw.
The likes of Slovan Bratislava's Robert Vittek, who has 23 goals to his name at international level, and captain Marek Hamsik of Napoli are likely to feature heavily if Slovakia are to spring a surprise.
Meanwhile, Zenit's Aleksandr Kerzhakov will be keen to find the net as he prepares to lead the line for Russia at the World Cup.
