The committee is one of those mandated by National Assembly chairman Cedric Frolick to probe corruption in departments and state-owned enterprises on their watch.
Zwane appeared before the committee once, in October 2017, but a second appearance in November was postponed after the controversial minister called in sick.
The committee could not subpoena Zwane to force him to appear, said committee chairman Sahlulele Luzipo.
In spite of the frustration expressed by the committee in November, Luzipo said legal advice was that because the minister had not declined to attend a hearing the committee had to set another date for him to appear.
If Zwane could not meet on that date he had to propose an alternative that would be subject to committee approval, he said.
The committee was unable to advance its work until Zwane had appeared, Luzipo said.
"We want to dispense with this matter as soon as possible, but we have been told we can't move without exhausting this matter with the minister.
"The committee has addressed the question: must we be kept stuck or should we say with the information at our disposal - can we do anything about it? We were told we should wait," he said.
"The committee is subject to the evidence of the minister to move ahead with its work."
Zwane has been firmly linked to irregular dealings with the Gupta family, which is closely tied to President Jacob Zuma, and has been alleged to wield undue and corrupt influence over certain state-owned firms.
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