Trace-element or heavy-metal pollution has emerged as a serious concern in terms of both environmental and human health issues. This study measured six trace and toxic heavy metals (Pb, Cd, Cr, Ni, Cu, and Zn) in four marine fish and shrimp species to assess their accumulation levels and evaluate the risks to human health. The mean concentrations of the metals in fish and shrimp species (Labeo bata, Sillaginopsis panijus, Platycepalus fuscus, and Penaeus monodon) followed the decreasing order of Zn (40.8 ± 9.7 μg/g) > Cu (17.8 ± 7.1 μg/g) > Pb (6.2 ± 1.8 μg/g) > Ni (0.4 ± 0.3 μg/g) > Cd (0.06 ± 0.02 μg/g > Cr (below detection level). Among the metals, only Pb in finfish and Pb, Cu, and Zn in shrimp samples exceeded the national recommended limits, representing possible risks to consumers. The mean metal concentrations in the studied fish/shrimp species followed the descending order of P. monodon > S. panijus > P. fuscus > L. bata, which implies that bottom dwellers and omnivores had higher levels of metals. However, the estimated daily intake (EDI) concentrations of Zn and Cu for the studied species were lower than the RDA (Recommended Daily Allowance). In addition, the Target Hazard Quotient (THQ) and hazard index (HI or TTHQ) values for all species were < 1, indicating that consumers might not experience carcinogenic health risks. A strong significant (p < 0.05) correlation between Cu and Pb (r = 0.623) and Zn and Cu (r = −0.871) indicated they were from the same source of origin. Cluster analysis (CA) and principal component analysis (PCA) demonstrated possible anthropogenic sources of toxic metals in the study area, specifically industrial wastes and agricultural chemicals.