The members took the decision following a meeting with the government over their concerns.
They said an agreement was reached with the government, hence the need to suspend the strike action.
In a statement, TEWU said: "the TEWU national leadership in consultation with the local executives of the public universities hereby resolve to suspend the industrial action embarked upon by the union in demand for some conditions of service."
It added: "We have come to an agreement with the government on the issues represented and therefore there is a need to suspend the strike action for now. We, therefore, call on our members on the various university campuses to resume work on the 19th of January 2021 while leadership continues to engage with government for the implementation of the agreement."