The talks were due to begin on 19 June, but the German official said they are likely to be delayed, even as the two-year negotiation clock continues to tick.
Others are saying that the result of Thursday's UK election has increased the likelihood of a soft Brexit, whereby Britain remains in the single market.
The general election delivered a hung parliament, with the Conservatives failing to obtain an overall majority. The latest BBC projection suggests the Conservative party will take around 318 seats, eight seats short of a parliamentary majority and 13 below their pre-vote majority.
Labour has won 261 seats, in line with the BBC forecast, gaining 29 seats on their 2015 performance. The Scottish National Party (SNP) took 35 seats in Scotland, a fall in 21 seats, with most losses going to the Conservative party.
Speaking to German radio, Oettinger, in charge of the budget and human resources, said, "We need a government that can act. With a weak negotiating partner, there's the danger than the negotiations will turn out badly for both sides. I expect more uncertainty now."
"We [the EU] are ready. It remains to be seen in the next hours whether the other negotiating side [the UK] can start too because without a government there no [Brexit] negotiations."
French Prime Minister Édouard Phillipe, however, said, "I don't believe that one should read into the result as a shift in the position expressed by the British over Brexit."
Speculation is mounting that, with the Tories unable to form a majority in Parliament, the Democratic Unionist Party - the largest unionist political party in Northern Ireland - might demand a softer Brexit to win its support in any coalition.
The former Ukip leader Nigel Farage insisted he would return to frontline politics if Brexit was threatened, as he criticised the Tories for picking a pro-Remain leader in Theresa May.
The MEP told BBC News, "What a huge error to pick a Remainer to lead a Brexit party at a Brexit election.
"It was a massive mistake, but I think that if we do get a Corbyn coalition then Brexit is in some trouble."
Asked whether he would return to the fray if Brexit was in trouble, Farage added, "I would have absolutely no choice but to do exactly that."
Meanwhile, only three of the 13 UK MEPs who stood in the poll have been elected to Westminster.
Anneliese Dodds, an MEP for Labour, will be shifting her career back home after winning Oxford East. Her group colleague Afzal Khan was elected in Manchester Gorton.
Conservative MEP Vicky Ford won the seat of Chelmsford. The ECR group member chairs the internal market and consumer protection committee. Andrew Lewer won in Northampton South.
Unsuccessful were Scottish Tory Ian Duncan; Ukip deputies Gerard Batten; Paul Nuttall; Tim Aker; Bill Etheridge; Stuart Agnew; Mike Hookem; Roger Helmer, and Greens member Molly Scott Cato.