Mr. Dickson also said a rumour on social media that the asylum seekers in Carrickfergus had arrived there from the Republic of Ireland was "simply not true".
Over the last few days, locals and people from other parts of Northern Ireland have been discussing the arrival of the asylum seekers on social media.
Some people took photographs of the asylum seekers and published these images on Facebook.
Mr. Dickson said, as a direct result of the photos being uploaded to social media, the Home Office had to move two of the asylum seekers to an undisclosed location.
"I am aware that a number of photographs have been taken where the asylum seekers are staying, at the Loughshore Hotel in Carrickfergus," said the East Antrim MLA on BBC Radio Ulster current affairs programme, Talkback.
"Sadly, two of the people who were placed in Carrickfergus were deemed at such a high risk as a result of those photographs that their families in their home country could now be at risk and they have had to be moved.
"This is how sensitive and how serious an issue this is - people really need to think before they do the sort of things they have been doing."
Liz Griffith from the Law Centre NI, who also appeared on the radio programme, was keen to stress the asylum seekers in Carrickfergus were there legally and appealed to local people to "think very carefully" before sharing images.
"The people who are being accommodated in Carrickfergus are under the care of the Home Office - this is completely separate to the Northern Ireland housing list and Housing Executive so it doesn't displace local people.
"I would urge people in Carrickfergus to think very carefully before taking photos of these people and sharing them on social media because we know authoritarian regimes around the world monitor local press and social media and so naming a person as an asylum seeker could put their families back home at risk - we have seen that happen, it is not theoretical.
"Be assured that the process is robust, all asylum seekers arriving here are quarantined, everyone is vetted and fingerprinted by the Home Office - security is taken very seriously."
A spokesperson for the Home Office said: "The asylum system is being exploited by criminal gangs who facilitate dangerous, unnecessary and illegal small boat crossings.
"Our nationality and borders bill will fix this broken system to deter those dangerous and illegal crossings.
"In the meantime, due to the unprecedented demand, we have had to use temporary accommodation such as hotels to manage demands on the asylum estates."