According to reports, at least two hotels in Kozhikode had to be shut down as migrant workers left for their states after receiving WhatsApp messages that they were not safe in Kerala.
The social media campaigns have been mostly going on in Kozhikode and Kochi.
"It has come to the government's notice that some anti- social elements are spreading rumours among migrant workers in Kerala. There are no confirmed reports of violence or any such unpleasant incidents in the state against them in the recent past," Vijayan said in a Facebook post.
He strongly condemned the attempts by those with vested interests to "tarnish" the image of Kerala by spreading unrest.
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Vijayan said district administrations and police have been directed to take action against spread of such rumours through social media.
Police would be vigilant on Facebook, Whatsapp, Twitter and other social media sites to track miscreants spreading such rumours, aiming to create unrest in society, he said.
Pointing out that migrant workers are well taken care of in Kerala, Vijayan said the state government had implemented many welfare schemes for them.
"On behalf of the people of Kerala and the government, I assure all migrant workers from other states once again that they are safe and are always welcome in Kerala," the chief minister said.
Labour Minister T P Ramakrishnan added that the government has already launched an enquiry on the source of such fake campaigns and strong action would be taken against those indulging in the same.
"Efforts are on to find out the source of such fake campaigns," he told reporters here.
"Such campaigns could be to portray the government in poor light," Ramakrishnan said.
There are estimated to be about 25 lakh to 30 lakh migrant workers in Kerala. The government has begun collecting data on them and there are plans to bring them under a medical insurance scheme.
Kerala DGP Loknath Behara, who spoke in Hindi and Bengali, urged workers not to panic and asked them to get in touch with the nearest police station or call him if they face any such situation.
"I have instituted an enquiry, knowing the limitations of technology. We will find out who is behind such campaigns," he added.