  Aims. We use the stellar line-of-sight velocities of Antlia B (Ant B), a
faint dwarf galaxy in the NGC 3109 association, to derive constraints on the
fundamental properties of scalar field dark matter (SFDM), which was originally
proposed to solve the small-scale problems faced by cold dark matter models.
Methods. We used the first spectroscopic observations of Ant B, a distant (d
$\sim$ 1.35 Mpc) faint dwarf ($M_\text{V} = -9.7$, $M_\star \sim
8\times10^5$M$_\odot$), from MUSE-Faint, a survey of ultra-faint dwarfs
conducted using the Multi Unit Spectroscopic Explorer. By measuring the
line-of-sight velocities of stars in the $1'\times 1'$ field of view, we
identified 127 stars as members of Ant B, which enabled us to model its dark
matter density profile with the Jeans modelling code GravSphere. We implemented
a model for SFDM into GravSphere and used this to place constraints on the
self-coupling strength of this model. Results. We find a virial mass of
${M_{200} \approx 1.66^{+2.51}_{-0.92}\times 10^9}$ $M_\odot$ and a
concentration parameter of ${c_{200}\approx 17.38^{+6.06}_{-4.20}}$ for Ant B.
These results are consistent with the mass-concentration relations in the
literature. We constrain the characteristic length scale of the repulsive
self-interaction $R_{\text{TF}}$ of the SFDM model to $R_{\text{TF}} \lesssim
180$ pc ($68\%$ confidence level), which translates to a self-coupling strength
of $\frac{g}{m^2c^4}\lesssim 5.2 \times 10^{-20}$ eV$^{-1}$cm$^3$. The
constraint on the characteristic length scale of the repulsive self-interaction
is inconsistent with the value required to match observations of the cores of
dwarf galaxies in the Local Group, suggesting that the cored density profiles
of those galaxies are not caused by SFDM.
