Bildt was to meet President Hamid Karzai and his Afghan counterpart Rangin Dadfar Spanta during the two-day visit, the European Union's Swedish presidency said in a statement.
Bildt and Holbrooke were to visit a European provincial reconstruction team, and the Swedish minister was also to meet "EU election observers ahead of the election on 20 August and with representatives of the EU police mission."
There are about 90,000 foreign troops - mainly US, British and Canadian - deployed in Afghanistan on a mission to stabilise the country as a Taliban insurgency reaches its deadliest heights since the 2001 US-led invasion.
There are a total of approximately 400 Swedish military personnel stationed in Afghanistan, according to the Swedish Armed Forces.
Ahead of next month's president election, the US military has launched one of its biggest offensives yet in Afghanistan, flying 4,000 Marines in to battle the Taliban in the southern province of Helmand.
Holbrooke, who arrived in Afghanistan Thursday, said the United States was working to avoid mistakes that allowed the vanquished Taliban to escape into Pakistan after they were toppled.