Qatar's Foreign Minister, Sheikh Mohammed Bin Abdulrahman al-Thani, told broadcaster Al Jazeera the country would "still have access to the world through international sea lanes and international airspace".
An anonymous Somali official told AP news agency at least 15 Qatar Airways flights had used Somalia's airspace on Monday, many more than on a normal day.
Who has done what?
The states who joined the move against Qatar, a tiny but gas-rich peninsula, on Monday include some of the biggest powers in the Arab world.
Saudi Arabia, Bahrain and the UAE closed all transport ties by air, land and sea to Qatar.
They gave all Qatari visitors and residents two weeks to leave their territory, and banned their citizens from travelling to Qatar.
The UAE and Egypt expelled Qatari diplomats, giving them 48 hours to leave.
What's caused the fall-out between Gulf neighbours?
Monday 5 June 2017, Saudi Arabia, Bahrain, Egypt, the UAE, and the internationally recognised Yemeni government severed their diplomatic relations with Qatar, accusing Doha of supporting terrorism.