  We study the entanglement entropy for open bosonic strings on multiple
$Dp$-branes by using the covariant open string field theory. Choosing one of
the spatial coordinates which are tangential to the hyperplane on which
$Dp$-branes are located, we divide the hyperplane into two halves. By using the
string wavefunction in the Fock space representation, we evaluate the
entanglement entropy. The entanglement entropy is found to be proportional to
the area of $(p-1)$-dimensional boundary of the bipartite hyperplanes and
divergent in the ultraviolet (UV) region as well as in the infrared (IR)
region. However, the leading divergences are mainly due to tachyon
contributions to the entanglement entropy, which may be absent in
supersymmetric string theories. Apart from the divergences thanks to tachyons,
the entanglement entropy for open bosonic strings on $Dp$-branes is finite for
$2 \le p \le d_{\text{critical}} -2$ and logarithmically divergent for $p =1,
d_{\text{critical}}-1$.
