Dockrell, 22, has been limited to seconds cricket at Taunton for much of this season in addition to his international commitments.
He joins a Sussex side fourth in the County Championship top tier.
"It's going to be an interesting few weeks in a new environment but it will be good to get some first-class cricket under my belt," Dockrell said.
"I've played a lot of second XI cricket in the last few years but to develop my game I need to be playing first XI cricket and this will give me the opportunity."
Somerset director of cricket Matt Maynard added: "George is a quality performer and has played a lot of international cricket but following the signing of Abdur Rehman he has had limited opportunities this year.
"This will be good for him and good for Somerset too."
Meanwhile, batsman Tom Abell has signed a four-year contract with Somerset, having progressed through the junior ranks to make his debut last season.
Sussex have signed Ireland spinner George Dockrell on a month-long loan from fellow Division One side Somerset.