The ministry said that the Turkish minister had called his Lithuanian counterpart, Linas Linkevičius, to apologize for the need to postpone the visit and to express his wish to arrange a visit in the near future on a date suitable for both sides.
Cavusoglu last visited Lithuania two years ago.
Linkevičius paid a visit to Turkey last August shortly after a failed coup attempt.
Turkey on Monday called for dialogue in resolving a worsening diplomatic crisis between Qatar and other Arab countries and offered to mediate in the process.
Saudi Arabia, Egypt, the United Arab Emirates and Bahrain on Monday severed diplomatic ties with Qatar, accusing it of supporting extremism. They were later joined by Yemen, Maldives, Mauritius and the government of the eastern part of Libya.