Data on the elemental composition of the diatom Chaetoceros spp. from natural phytoplankton communities of Arctic marine ecosystems are presented for the first time. Samples were collected during the 69th cruise (22 August–26 September 2017) of the R/V Akademik Mstislav Keldysh in the Kara, Laptev, and East Siberian Seas. The multi-element composition of the diatom microalgae was studied by ICP-AES and ICP-MS methods. The contents of major (Na, Mg, Al, Si, P, S, K and Ca), trace (Li, Be, B, Ti, V, Cr, Mn, Co, Ni, Cu, Zn, Ga, As, Se, Rb, Sr, Mo, Ag, Cd, Sn, Sb, Cs, Ba, Hg, Tl, Pb, Bi, Th and U) and rare earth (Sc, Y, La, Ce, Pr, Nd, Sm, Eu, Gd, Tb, Dy, Ho, Er, Tm, Yb, and Lu) elements varied greatly, which was probably associated with the peculiarities of the functional state and mineral nutrition of phytoplankton in the autumn period. Biogenic silicon was the dominant component of the chemical composition of Chaetoceros spp., averaging 19.10 ± 0.58% of dry weight (DW). Other significant macronutrients were alkaline (Na and K) and alkaline earth (Ca and Mg) metals as well as biogenic (S and P) and essential (Al and Fe) elements. Their total contents varied from 1.26 to 2.72% DW, averaging 2.07 ± 0.43% DW. The Al:Si ratio for natural assemblages of Chaetoceros spp. of the shelf seas of the Arctic Ocean was 5.8 × 10−3. The total concentrations of trace and rare earth elements on average were 654.42 ± 120.07 and 4.14 ± 1.37 μg g−1 DW, respectively. We summarize the scarce data on the average chemical composition of marine and oceanic phytoplankton and discuss the limitations and approaches of such studies. We conclude on the lack of data and the need for further targeted studies on this issue.