The recount, which was requested by Green Party candidate Jill Stein, who received a minute fraction of the total vote, flew in the face of an election "that has already been conceded," Trump said.
Hillary Clinton's campaign said it would join the recount although it has not seen any irregularities so far in the White House contest won by Trump.
Marc Erik Elias, an election lawyer for the Democratic candidate, said in a post on Medium.com that the campaign would also participate in recounts in the closely contested states of Michigan and Pennsylvania if they are arranged.
Stein has also announced plans to seek recounts in those two states.
In a statement, Trump asserted that "the people have spoken and the election is over, and as Hillary Clinton herself said on election night, in addition to her conceding by congratulating me, 'We must accept this result and then look to the future.'"
Trump, the Republican presidential candidate, won Michigan, Pennsylvania and Wisconsin by a total of just over 100,000 votes. The razor-thin victories in those states pushed him above the 270 votes needed for victory in the Electoral College.
"It is important to point out that with the help of millions of voters across the country, we won 306 electoral votes on Election Day -- the most of any Republican since 1988," Trump said.
"This is a scam by the Green Party for an election that has already been conceded, and the results of this election should be respected instead of being challenged and abused, which is exactly what Jill Stein is doing," Trump added.
However, during the campaign Trump himself threatened to reject the result if he lost, alleging that the race was "rigged" by the media and the establishment elite.
Elias, the Clinton counsel, said that "because we had not uncovered any actionable evidence of hacking or outside attempts to alter the voting technology, we had not planned to exercise this option ourselves."
"But now that a recount has been initiated in Wisconsin, we intend to participate in order to ensure the process proceeds in a manner that is fair to all sides," he added.
It was not immediately clear how the Clinton campaign plans to take part in the recount.
Although experts say there is virtually no chance of overturning the final result, the recounts could reignite debate over the legitimacy of Trump's election, already fueled by Clinton's lead in the popular vote, which now stands at more than two million.
Clinton lost by around 20,000 votes in Wisconsin, 70,000 votes in Pennsylvania and 10,000 votes in Michigan.
Elias noted that Trump's 10,000-vote lead in Michigan "well exceeds the largest margin ever overcome in a recount."
Elias said the Clinton campaign had been conducting its own investigation of the election results after receiving "hundreds of messages, emails, and calls urging us to do something, anything, to investigate claims that the election results were hacked and altered in a way to disadvantage Secretary Clinton."
But he said the Clinton campaign had seen no evidence so far the election results had been manipulated in Trump's favor.
Stein has cited unspecified "anomalies" as grounds to mount a challenge to the November 8 election results in Michigan, Pennsylvania and Wisconsin.
"After a divisive and painful presidential race, reported hacks into voter and party databases and individual email accounts are causing many Americans to wonder if our election results are reliable," Stein said on her website.
On Saturday she told CNN that "going into this election, and throughout the election, we saw hacking taking place all over the place, of state voter databases, of the democratic party's vote database, of private e-mail accounts. This was a hack-riddled election."