A 26-year-old man has been arrested after health minister Robin Swann was threatened online.
The BBC's Stephen Nolan show reported that sectarian threats had been made against Mr Swann and his family.
It is understood a pro-IRA slogan was sent to the minister, who is leading Northern Ireland's fight against the coronavirus.
In a statement, the PSNI said: "Police are investigating after threatening and offensive comments were made on a social media platform on Friday April 3.
"A 26-year-old man was arrested in the Ballymena area on Sunday on suspicion of improper use of telecommunications causing anxiety and subsequently released on police bail pending further enquiries.
"The investigation is ongoing."
The Department of Health added: "The department can confirm that a threatening communication was received by the minister via social media. This matter has been passed to the police. The department will not be making any further comment.”
Mr Swann's party colleague, UUP leader Steve Aiken said: "It is utterly despicable that threats that were blatantly intimidating and sectarian were made against our exceptionally hard-working and dedicated health minister."
Sinn Fein deputy leader Michelle O'Neill and SDLP leader Column Eastwood have condemned the threats.
Mr Eastwood said Mr Swann was "working night and day to reduce the impact of Coronavirus on our communities".
"The vile sectarian abuse and threats that he and his family have been subjected to are disgusting and those responsible must be held accountable," he said.
“On behalf of the SDLP, I want to express our solidarity with Robin and his family.”
Ms O'Neill described the abuse and threats as "disgraceful"
"Solidarity to Robin and his family," she tweeted.
The disgraceful abuse and threats against health minister Robin Swann are to be condemned.
— Michelle O’Neill (@moneillsf) April 6, 2020
In very turbulent and challenging times there is no place for this nonsense as we work together to save lives.
Solidarity to Robin and his family.
DUP leader Arlene Foster described the threat as "vile and disgusting".
This is vile and disgusting. Especially at a time when we are focused on protecting life and getting Northern Ireland through Covid-19. https://t.co/uMdf5j3c8o
— Arlene Foster (@DUPleader) April 6, 2020
Alliance MLA Paula Bradshaw said she was horrifed by the online abuse.
Horrified to hear of the abuse online against Robin Swann MLA - we all need to pull together and work to minimising the impact from this pandemic.
— Paula Bradshaw MLA (@PaulaJaneB) April 6, 2020
This is an incredibly challenging and stressful time, not least for your Health Minister.
Robin Swann is a decent, genuine politician working round the clock trying to save lives. Neither he nor his family deserve this. https://t.co/DPsyuitXiw
— Philip McGuigan (@mcguigan_philip) April 6, 2020
Secretary of State Brandon Lewis said Mr Swann was working hard to protect the public during the coronavirus pandemic.
I utterly condemn the sinister messages to @RobinSwannMoH and his family. All public representatives should be allowed to serve the people who elected them without fear or intimidation. Robin is working hard to protect the public & online abuse will not deter him.
— Brandon Lewis #StayHomeSaveLives (@BrandonLewis) April 6, 2020
