Yes, Virginia.  Paintings do have rhythm.

There is flowing rhythm, staccato rhythm, rhythm with counterpoint and rhythm carried by a "bassline".  Each gives its own quality of movement within an art work and becomes an integral part of the experience given to a viewer.

In visual art, staccata works very much the same as in music.  It is created by a motif repeated rapidly, forming a texture or a sequence of small shapes, causing the eye to move rapidly within the piece.

Look at these two renditions of my painting, Snacktime.

The version on the left is just a squirrel perched in a motionless background doing nothing more than surrounding the squirrel. But in the version on the right, the background plays a rhythmic role, using a staccato rhythm created with a motif of repeated tiny shapes.  These little shapes composed with colors found in the squirrel add action and life to the entire painting by creating a rapid rhythmic movement around the squirrel.

Another more subtle rhythm is the "bassline,"  my own invented term for a background movement that supports the main rhythm of the painting.  I used the "bassline" to support the reversed-S flowing rhythm in my painting, Touch of Gold.  

Touch of Gold    Oil on Canvas

Flowing rhythm in a reversed-S pattern

The "bassline" in music is the background bass that supports the piece, not always noticeable, but the piece would be shallow without it.  In painting, it's a visual rhythm created by background material visable within the mail content, such as sky or a repeated color or value, something that we don't necessarily notice, but without it the painting would seem lacking.  Below, on the left I've taking out the "bassline."  Notice how closed the frontal tree feels without areas of sky poking through.

Rhythm in visual art is visual movement that guides the pacing of the eye just like movement in music guides the flow of the piece.  Look for it.  It's everywhere!