"Several Ghanaian nationals have in recent days attempted to cross into Lithuania without visas, but they were sent back," he told reporters.
This marks the first incident related to Lithuanian officials' efforts to prevent football fans from illegally traveling between mainland Russia and Kaliningrad during the World Cup, which is starting this week.
Kaliningrad will host four group stage matches -- Croatia vs Nigeria, Serbia vs Switzerland, Spain vs Morocco, and England vs Belgium -- between June 16 and 28.
It is believed that fans of these teams will make up the bulk of tourists travelling to Kaliningrad during that period. Some of them may also travel from the exclave to mainland Russia.
Lithuanian officials are mostly concerned about third-country nationals, who need Schengen visas to cross Lithuania's territory.
Lithuanian Interior Minister Eimutis Misiūnas said on Monday that the country's authorities were ready for all possible scenarios.
"We practically have no weak spots," he said after meeting with representatives from all bodies responsible for preparations for the World Cup.
Lithuanian officials have in recent months held drills and coordinated efforts with their Russian counterparts to prepare for managing increased migration flows to Kaliningrad.
The border guard chief also said that they had also prepared themselves for dealing with other types of violations, such as public display of Soviet symbols, which is banned in Lithuania.