Officers were called to his constituency office in East Dunbartonshire on Tuesday afternoon.
Police set up a temporary cordon around the Townhead area in Kirkintilloch, although it has since been removed.
The package has been taken for examination by police. Mr Nicolson was last elected to represent the area at Westminster in May 2015.
In a tweet, Mr Nicolson said: "Everyone is ok. The police were speedy and efficient and took away the package."

Her son Bryce, 23, was flying off on a dream holiday in Bali with the "love of his life", 21-year-old Daisy Oehlers. "They were heading for paradise and never came back."
They were among 298 who lost their lives when the Malaysia Airlines plane was shot out of the sky over eastern Ukraine on 17 July 2014.
No-one has yet been prosecuted for the attack but the Dutch-led joint investigation team says it has identified a list of 100 "persons of interest". They say the plane was brought down by a Buk missile brought in from Russian territory and fired from a field in the hands of pro-Russian rebels.
The memorial site, the first official monument chosen by their families, is a short drive from Schiphol airport, where three years ago to the day many would have waved their final goodbyes.
Two-hundred-and-ninety-eight trees have been planted. One to represent each victim. They were either planted by the relatives themselves or decorated by them with flowers and butterfly mobiles.
The young forest at Vijfhuizen is designed to symbolise life, growth and hope and offer a permanent place full of life to remember the dead. At the heart of the forest is a monument in the shape of an eye. Each of the 298 victims' names is engraved in the iris pointing upwards.
Above the forest the blue sky was streaked with white aircraft trails, and the air filled with the constant rumble of jet engines as King Willem-Alexander, Queen Maxima and Prime Minister Mark Rutte joined an estimated 2,000 relatives for a moving ceremony.
All 298 names were read out by relatives, their voices faltering and often breaking.
As the Royal Netherlands air force orchestra played, the king and queen joined local children placing sunflowers at the foot of the monument. The flowers are a poignant symbol for the families as much of the wreckage of flight MH17 came down in a field bordered by sunflowers.
Monday's ceremony marked the third anniversary of the disaster but many relatives hoped these high profile events would keep what happened in the public consciousness and maintain pressure on the authorities to track down the culprits.
The Dutch-led Joint Investigation Team (JIT) has confirmed the rocket was smuggled in from Russia, fired from a field in territory controlled by Russian backed rebels at the time.
But they still have not named any suspects. Many of the families are struggling to keep their faith in the international community's ability to bring to justice the people who carried out the attack.
Malaysia's transport minister hinted the first arrest warrants may be issued later this year or early in 2018.  There has been no confirmation from the Dutch prosecutors leading the criminal investigation.
Russia vetoed a UN Security Council resolution in 2015 to establish an international tribunal.
Instead members of the JIT have agreed that any future trials will be conducted in the Netherlands in accordance with Dutch law - which means the accused could be tried in absentia.
If the suspects are in Russia, few believe they will be extradited. The victims' relatives will also be offered the chance to speak in court.
Russia and the pro-Russian rebels in the east deny any involvement in the rocket attack. But on Monday Ukrainian President Petro Poroshenko said Russia must be held to account.
Addressing the families, Evert van Zijtveld said the memorial was a tangible, permanent place to reflect. His teenage son, daughter and parents-in-law were on board MH17.
"With the sun, rain and fertile earth," he told the audience, "the trees will flourish and allow our loved ones to live on in our hearts."
Police are investigating a suspicious package delivered to the office of the SNP's John Nicolson.
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"It's so important not to forget but remembering brings all the memories flooding back," said Silene Fredriksz, as relatives came from across the world to mark the first official monument in the Netherlands to those who died on flight MH17.