The adverts appeared in at least three Arabic-language newspapers and one English-language daily in Lebanon on Monday.
"Denmark has decided to tighten the regulations concerning refugees in a number of areas," the advert cautions.
It notes that social benefits for newly-arrived refugees are being reduced "by up to 50 percent" and that family reunification for those with temporary residence permits is not allowed for the first year after they arrive.
It advises would-be migrants and refugees that they will be required to speak and understand Danish to obtain a permanent residency.
"All rejected asylum seekers must be returned quickly from Denmark," it adds.
"There is a special return centre for rejected asylum seekers to ensure (they)... leave Denmark as quickly as possible."
In Denmark, Immigration and Integration Minister Inger Stojberg, an immigration hardliner from the right-wing Venstre party, announced the adverts on Facebook.
"Today I have, as promised, published advertisements in four Lebanese newspapers informing about the changed conditions for people who apply for asylum in Denmark," she wrote.
She said the text would also be placed in asylum centres in Denmark in 10 different languages and spread on social media.
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"The aim is to inform objectively and soberly about (Danish rules), which the government is in the process of tightening," she added.
"In light of the huge influx to Europe these days, there is good reason for us to tighten rules and get that effectively communicated."
Her Facebook post garnered over 5,000 likes, though some left critical comments.
"You should be ashamed," wrote Dorthe Agertoug in the southeastern town of Koge.
"One of the greatest humanitarian catastrophes in recent times and our government's answer is to publish advertisements. It's a parody," added Vivi Ravnskjaer Terp in the southwestern town of Vojens.
A spokeswoman for Denmark's integration ministry denied a report that five major newspapers in Turkey had refused to carry the adverts.
Denmark's minority right-wing government relies on the backing of the anti-immigrant Danish People's Party to pass legislation.
It slashed benefits for asylum seekers this month in a bid to bring down the number of refugees coming to the Scandinavian country.
The adverts were placed as several European nations opened their doors to a wave of migrants and refugees, or announced new quotas to accept those in need of asylum.
Lebanon, with a population of just four million, is hosting more than 1.1 million Syrian refugees.
Some 11 million Syrians have been displaced from their homes by the conflict that began in March 2011, with four million becoming refugees.