In the introduction of the Logjam paper, it is stated that
After a week-long precomputation for a specified 512-bit
group, we can compute arbitrary discrete logs in that group
in about a minute.
So it seems that what it actually does is attack the discrete logarithm problem, so any discrete-logarithm-based system which uses a common prime should be equally vulnerable. In particular, in Section 3.2 of RFC 5054, it is stated that
An attacker who could calculate discrete logarithms
% N could compromise user passwords, and could also compromise the confidentiality and integrity of TLS sessions. Clients MUST ensure that the received parameter
N is large enough to make calculating discrete logarithms computationally infeasible.
Since RFC5054 specifies only one prime for each bit-length, it will indeed be vulnerable. Even though it does not specify a 512-bit prime, it does specify a 1024-bit one, which is considered vulnerable by the Logjam authors:
We estimate that even in the 1024-bit case, the computations are plausible given nation-state resources
Using a prime of at least 1536 bits should be sufficient to thwart such attacks, since there is no known "downgrade" attack on SRP.