We provide a measurement of the $6s6p\phantom{\rule{0.16em}{0ex}}^{3}P_{0}--5d6s\phantom{\rule{0.16em}{0ex}}^{3}D_{1}$ transition in multiple isotopes of ytterbium (Yb) at 1389 nm. We measure the absolute frequencies of $^{170}\mathrm{Yb}$, $^{171}\mathrm{Yb}$ (1/2--1/2), $^{171}\mathrm{Yb}$ (1/2--3/2), $^{172}\mathrm{Yb}$, $^{173}\mathrm{Yb}$ (5/2--3/2), $^{173}\mathrm{Yb}$ (5/2--5/2), $^{173}\mathrm{Yb}$ (5/2--7/2), $^{174}\mathrm{Yb}$, $^{176}\mathrm{Yb}$ $6s6p\phantom{\rule{0.16em}{0ex}}^{3}P_{0}--5d6s\phantom{\rule{0.16em}{0ex}}^{3}D_{1}$ transitions with modulation transfer spectroscopy (MTS) in a hollow cathode lamp. High-resolution dispersive signals of the MTS are obtained for all the stable isotopes, except for low-abundance $^{168}\mathrm{Yb}$. The frequencies of these transitions are measured from the beat signals between a stabilized optical frequency comb and the MTS-locked laser, and the systematic shifts therein are corrected. The hyperfine components $^{173}\mathrm{Yb}$ (5/2--5/2) and $^{171}\mathrm{Yb}$ (1/2--3/2) of the $6s6p\phantom{\rule{0.16em}{0ex}}^{3}P_{0}--5d6s\phantom{\rule{0.16em}{0ex}}^{3}D_{1}$ transition for $^{173}\mathrm{Yb}$ and $^{171}\mathrm{Yb}$ isotopes overlap to form an overlapped line; we determine their frequencies by a fitting method. The isotope shifts relative to $^{174}\mathrm{Yb}$ are determined as 284.5(20) MHz for $^{170}\mathrm{Yb}$, 121.5(7) MHz for $^{172}\mathrm{Yb}$ and \ensuremath{-}114.6(6) MHz for $^{176}\mathrm{Yb}$. The hyperfine constants of the $5d6s\phantom{\rule{0.16em}{0ex}}^{3}D_{1}$ state are determined as $A(^{171}\mathrm{Yb})=\ensuremath{-}2039.4(7)\phantom{\rule{0.16em}{0ex}}\mathrm{MHz}$, $A(^{173}\mathrm{Yb})=563.5(2)\phantom{\rule{0.16em}{0ex}}\mathrm{MHz}$, and $B(^{173}\mathrm{Yb})=336.8(3)\phantom{\rule{0.16em}{0ex}}\mathrm{MHz}$.