We present the results of a search for short and intermediate-duration gravitational-wave signals from four magnetar bursts in Advanced LIGO's second observing run. We find no evidence of a signal and set upper bounds on the root sum squared of the total dimensionless strain ($h_{\text{rss}}$) from incoming intermediate-duration gravitational waves ranging from $1.1 \times 10^{-22}$ at 150\,Hz to $4.4 \times 10^{-22}$ at 1550\,Hz at 50\% detection efficiency. From the known distance to the magnetar SGR 1806-20 (8.7 kpc) we can place upper bounds on the isotropic gravitational wave energy of $3.4 \times 10^{44} \text{erg}$ at 150\,Hz assuming optimal orientation. This represents an improvement of about a factor of 10 in strain sensitivity from the previous search for such signals, conducted during initial LIGO's sixth science run. The short duration search yielded upper limits of $2.1 \times 10^{44} \,\text{erg}$ for short white noise bursts, and $2.3\times 10^{47}\,\text{erg}$ for $100 \, \text{ms}$ long ringdowns at 1500\,Hz, both at 50\% detection efficiency.