The EU's ambassador to Sudan is veteran Irish diplomat Aidan O'Hara.
"A few hours ago, the EU Ambassador in Sudan was assaulted in his own residency," Borrell wrote on Twitter, without detailing any injuries to the envoy.
"Security of diplomatic premises and staff is a primary responsibility of Sudanese authorities and an obligation under international law," he added.
EU spokeswoman Nabila Massrali told AFP that the ambassador was "OK" following the assault.
"The security of the staff is our priority," she said. "The EU delegation has not been evacuated. Security measures are being assessed."
Fighting between the Sudanese army and a rival paramilitary faction has killed around 200 people and wounded 1,800 after three days of urban warfare.
The United Nations has called for an immediate ceasefire and international bodies, including the European Union, have expressed grave concern.