News of the incident came as Dungannon hosted a major beef industry event yesterday (Tuesday) and less than two months after a similar find on farmland in Co Armagh, which is believed to have been a deliberate attempt to infect local herds with brucellosis.
DARD confirmed that the latest incident, which occurred over the weekend, is currently being investigated by the PSNI.
Reacting to the find, the Agriculture and Rural Development Minister Michelle Gildernew MP MLA said she was appalled by the "irresponsible action and the clear intent" of the perpetrators and she said such illegal actions threaten farming families and their animals.
"We will follow up this latest incident as rigorously as possible. The PSNI have carried out preliminary investigations as well as forensic analysis of the scene and the foetus itself is undergoing laboratory testing for brucellosis before DNA analysis is carried out," she added.
"While the motive for this is not obvious, what is clear is that there are those in the farming community prepared to deliberately break the laws intended to protect farmers, their families and their animals for their own motives.
"If this latest incident does anything it is to underline how little regard the individuals, who take this sort of action, have for the whole farming and rural community. The PSNI are taking these incidents very seriously and both cases are under active investigation.
"The fact that on this occasion a member of my veterinary staff was deliberately targeted will not deflect our efforts to pursue those responsible and only strengthens our resolve to catch the perpetrators."
Concluding her statement the minister said: "This sinister incident follows the finding of a foetus, dumped in similar circumstances in a field in Lislea, Co Armagh in January.
"I find this behaviour totally unacceptable and cannot understand why these individuals continue to risk our local cattle industry. We must all be on our guard against these attacks and I wish to renew my appeal for help to the public, for anyone who has any information about these incidents to contact the PSNI or DARD.
"It is important that the entire farming community unite against this sort of reckless and illegal behaviour and assist us in any way possible so that together we can eradicate brucellosis from the island of Ireland."
Tom Elliott, who is the MLA for the area as well as the deputy chairman of the Committee for Agriculture and Rural Development, has spoken of his shock at the latest development.
"This is an utterly shocking development. The fact that who ever is responsible dumped this foetus at the DARD veterinary official's house is very sinister indeed. They have taken time to find out the address of this official and then went to the trouble of leaving the foetus," he added.
"It is very worrying given that another foetus was dumped at a farm in Co Armagh in a deliberate attempt to infect a herd there back in January.
"I am not sure just how far DARD and the police have progressed with their investigation into the incident in January but I hope that what has happened in Dungannon is in no way connected. If they are then it is a very worrying development indeed."
Mr Elliott called on DARD and the PSNI to step up what they are doing to bring those responsible for dumping the calf foetuses to be brought to justice.
He said: "Every stop must be pulled out now. DARD and the police must do much more to ensure the culprits of both these incidents are brought before the full rigours of the law."
Meanwhile, Ulster Farmers' Union president Graham Furey has added to the condemnation.
Mr Furey said: "The Ulster Farmers' Union totally condemns this action as it defies any logic and we do not believe any right minded farmer would be involved in such an activity.
"It is difficult to understand the motivation behind this event but our position has always been to reduce the potential for disease spread. Such activity is completely contrary to this."