A statement from Tunisia's interior ministry said the three were members of a 'terrorist cell connected to the terrorist Anis Amri who carried out the terrorist attack in Berlin'.
The ministry said Amri had sent Fedi money to join him in Europe.
It is unclear whether the suspects helped Amri flee Berlin. The interior ministry said Amri had sent money to his nephew and encouraged him to pledge allegiance to ISIS.
'One of the members of the cell is the son of the sister of the terrorist (Amri) and during the investigation he admitted that he was in contact with his uncle through (the messaging service) Telegram,' it said.
Amri allegedly urged his nephew to adopt jihadist 'takfiri' ideology and 'asked him to pledge allegiance to Daesh (IS),' it said.
The nephew also told investigators that Amri 'sent him money through the post... so that he could join him in Germany,' the statement added.
The ministry claimed the arrested man said his uncle was the 'prince' or leader of a jihadist group based in Germany and known as the 'Abu al-Walaa' brigade.
The terrorist's nephew was arrested in Amri's hometown of Oueslatia, while the others were arrested in Tunis.
The arrests happened hours after the mother of 24-year-old Amri - who was yesterday shot to death by police in Milan - said the world will never know why he carried out the mass killing.
Nour El Houda Hassani, speaking at Amri's hometown of Oueslatia in Tunisia said that a 'great secret' had died with him.
Family members have questioned the need to kill the terrorist.
His mother said: 'Within him is a great secret. They killed him, and buried the secret with him.'
And she called on authorities to unearth who had put her son up to the attack, stating: 'I want the truth about my son. Who was behind him?'
Amri's brother Abdel Kader wept as he questioned the need to kill him.
He said: 'My brother is dead. Bring us his remains, even one of his fingers, and I will put it in my pocket. They killed him when he was still only a suspect. Why?'
Yesterday family members spoke of their shock over Amri's death, and his radicalisation.
Abdul Kader said his sibling died 'the day he swore allegiance to Daesh' - a derogatory name for ISIS.
Speaking after news of the 24-year-old's death reached his family in Tunisia, Abdul said: 'He did not call us when they published his picture - that's what convinced us that he was the one who carried out this terrorist attack.
'We are sorry for the death of Anis, but he did not die today, he died the day after he swore allegiance to Daesh.
'I know he had a criminal record but I didn't think that he would ever become a terrorist.'