Journalist Jamal Khashoggi was killed in a fight in the Saudi consulate in Istanbul, the country's state TV reported quoting an initial probe.
It said deputy intelligence chief Ahmad al-Assiri and Saud al-Qahtani, senior aide to Crown Prince Mohammed Bin Salman, were dismissed over the affair.
US President Donald Trump said what happened was "unacceptable" but Saudi Arabia was a "great ally".
This is the first time the kingdom has admitted Mr Khashoggi has died.
Speaking at a round table event, President Trump said the arrests were an important "first step". He praised the kingdom for acting quickly, and while he said sanctions were an option against the country, he spoke of the possible effect such moves would have on the US economy.
Asked if he found Saudi Arabia's version of events credible, he replied, "I do."
Saudi King Salman has also reportedly ordered the formation of a ministerial committee, headed by Crown Prince Mohammed, to restructure the intelligence services.
The journalist was last seen entering the Saudi consulate in Istanbul on 2 October, to pick up paperwork that would allow him to marry his fiancée Hatice Cengiz.
Reports on Saudi state media followed shortly after King Salman spoke on the phone to Turkey's President Recep Tayyip Erdogan about the case.
Saudi Arabia reportedly acted on information provided by Turkish authorities as part of its inquiry, investigating a number of suspects.
A statement from Saudi Arabia's public prosecutor said a fight broke out between Mr Khashoggi and people who met him in the consulate - ending with his death.
The investigations are still underway, it said, and 18 Saudi nationals have been arrested.
Media reports also spoke of the dismissal of the two senior officials.
Saud al-Qahtani is a prominent member of the Saudi Royal Court and adviser to Prince Mohammed bin Salman.