According to the prosecution, the case involves claims that vulnerable individuals were lured with promises of better opportunities abroad.
Investigators believe that some of those recruited may not have been fully informed about the true nature of the arrangements before leaving the country.
Authorities say they are working to establish the full extent of the alleged operation.
During the court session, state lawyers argued that releasing Omwamba at this stage could interfere with witnesses or disrupt ongoing investigations.
They urged the court to give them more time to gather evidence and record statements from those who may have been affected.
The defense team, however, maintained that their client is innocent and has the right to bail.
They told the court that Omwamba is willing to cooperate with investigators and attend all required court sessions.
His lawyers are expected to formally present arguments in support of his release when the bail hearing takes place next week.
In delivering the ruling, the magistrate directed that the accused be remanded at Kiambu Remand Prison until March 5, when the court will consider the bail request.
The magistrate noted that the decision was meant to balance the rights of the accused with the need to protect the integrity of the investigations.
Human trafficking remains a serious concern in Kenya, with authorities warning citizens to be cautious about offers of jobs or travel opportunities abroad that seem too good to be true.
Government agencies have repeatedly advised Kenyans to verify recruitment agencies and ensure that all travel documents are processed through the proper legal channels.
The case has drawn public attention, especially among families with relatives seeking work overseas.
Many are now waiting to see how the court proceedings will unfold and whether more suspects could be linked to the alleged network.