Parolin, who is on a visit in Lithuania, is also to pay tribute at the January 13 memorial and the Museum of Genocide Victims in Vilnius.
President Grybauskaitė is to discuss global politics, terrorism and aid to war refugees with the Vatican official.
Parolin has come to Lithuania to take part in the three-day Catholic Church event, the National Congress of Mercy.
On Monday, he is also delivering a speech on the Holy See's diplomatic activities at Vilnius University (in English).
Parolin has said that Pope Francis could be visiting Lithuania soon, too.
"As I said at the Hill of Crosses yesterday, I am like John the Baptist who paves the way. I am praying for the pope to visit the land as soon as possible," Parolin said during a service at the Vilnius Cathedral Square on Sunday.
At a meeting with the cardinal on Saturday, Lithuania's Prime Minister Algirdas Butkevičius said it would be great to host the pope in Lithuania "in 2018 when the country marks 100-year anniversary of its statehood".
Butkevičius also said that Parolin's visit was a historic event. This is the first visit by a top-ranking Vatican official in Lithuania since Pope John Paul II came to Lithuania in 1993.