diff --git a/pkg/cmd/roachtest/tests/follower_reads.go b/pkg/cmd/roachtest/tests/follower_reads.go
index 3a2febcff258..b31c0a2c32a8 100644
--- a/pkg/cmd/roachtest/tests/follower_reads.go
+++ b/pkg/cmd/roachtest/tests/follower_reads.go
@@ -1008,6 +1008,13 @@ func runFollowerReadsMixedVersionGlobalTableTest(
 		// Use a longer upgrade timeout to give the migrations enough time to finish
 		// considering the cross-region latency.
 		mixedversion.UpgradeTimeout(60*time.Minute),
+
+		// This test is flaky when upgrading from v23.1 to v23.2 for follower
+		// reads in shared-process deployments. There were a number of changes
+		// to tenant health checks since then which appear to have addressed
+		// this issue.
+		mixedversion.MinimumSupportedVersion("v23.2.0"),
+
 		// This test does not currently work with shared-process
 		// deployments (#129167), so we do not run it in separate-process
 		// mode either to reduce noise. We should reevaluate once the test