jats:titleAbstract</jats:title>jats:pWe prove that the geodesics associated with any metric generated from Liouville quantum gravity (LQG) which satisfies certain natural hypotheses are necessarily singular with respect to the law of any type of jats:inline-formulajats:alternativesjats:tex-math$$\mathrm{SLE}_\kappa $$</jats:tex-math><mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> mml:msub mml:miSLE</mml:mi> mml:miκ</mml:mi> </mml:msub> </mml:math></jats:alternatives></jats:inline-formula>. These hypotheses are satisfied by the LQG metric for jats:inline-formulajats:alternativesjats:tex-math$$\gamma =\sqrt{8/3}$$</jats:tex-math><mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> mml:mrow mml:miγ</mml:mi> mml:mo=</mml:mo> mml:msqrt mml:mrow mml:mn8</mml:mn> mml:mo/</mml:mo> mml:mn3</mml:mn> </mml:mrow> </mml:msqrt> </mml:mrow> </mml:math></jats:alternatives></jats:inline-formula> constructed by the first author and Sheffield, and subsequent work by Gwynne and the first author has shown that there is a unique metric which satisfies these hypotheses for each jats:inline-formulajats:alternativesjats:tex-math$$\gamma \in (0,2)$$</jats:tex-math><mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> mml:mrow mml:miγ</mml:mi> mml:mo∈</mml:mo> mml:mo(</mml:mo> mml:mn0</mml:mn> mml:mo,</mml:mo> mml:mn2</mml:mn> mml:mo)</mml:mo> </mml:mrow> </mml:math></jats:alternatives></jats:inline-formula>. As a consequence of our analysis, we also establish certain regularity properties of LQG geodesics which imply, among other things, that they are conformally removable.</jats:p>