The agency also noted increased tensions with long-time rival Iran and greater uncertainty over economic policy, now overseen by Deputy Crown Prince Mohammed bin Salman.
Fitch downgraded the kingdom's credit rating to AA- from AA, which still denotes expectations of very low default risk.
The outlook remains negative, indicating a further cut is likely.
Fitch said it had revised downwards its oil price assumptions for this year and next, to $35 and $45 a barrel, which "has major negative implications for Saudi Arabia's fiscal and external balances".
In February another agency, Standard and Poor's, cut the kingdom's credit rating by two notches, to A-, citing the impact of lower oil prices on the kingdom's finances.
Last month, Moody's placed Saudi Arabia and other Gulf oil producers on review for downgrades.
Oil prices have collapsed from above $100 in early 2014, and on Tuesday traded at just over $40.
Signup to our newsletter and follow us on Facebook and Twitter!
The government has said oil income made up 73 percent of revenue in 2015, compared with an average of 90 percent in the previous decade.
The kingdom reported a record budget deficit of $98 billion last year and projects a shortfall of $87 billion in 2016.
To cope with the gap it raised retail fuel prices by up to 80 percent in December and cut subsidies to electricity, water and other services.
It has also delayed some major projects under King Salman, who acceded to the throne last year.
Salman named his son Prince Mohammed to posts including defence minister and head of the Council of Economic and Development Affairs.
"Control over economic policy making has been concentrated in the hands of Prince Mohammed," Fitch said.
"This may have contributed to an acceleration of the economic policymaking process, but has also reduced the predictability of decision-making."
The agency also noted that Saudi Arabia faces high geopolitical risks relative to AA-rated peers.
"Tensions have risen between Saudi Arabia and its long-standing regional rival Iran, and are expected to persist, although a direct confrontation is highly unlikely. Saudi Arabia's military intervention in Yemen and in Syria shows a greater assertiveness in foreign policy."