diff --git a/store/postgres/src/catalog.rs b/store/postgres/src/catalog.rs
index 22bf3d941ef..99e1fbb604d 100644
--- a/store/postgres/src/catalog.rs
+++ b/store/postgres/src/catalog.rs
@@ -11,6 +11,7 @@ use std::collections::{HashMap, HashSet};
 use std::fmt::Write;
 use std::iter::FromIterator;
 use std::sync::Arc;
+use std::time::Duration;
 
 use graph::prelude::anyhow::anyhow;
 use graph::{
@@ -616,3 +617,27 @@ pub fn stats(conn: &PgConnection, namespace: &Namespace) -> Result<Vec<VersionSt
 
     Ok(stats.into_iter().map(|s| s.into()).collect())
 }
+
+/// Return by how much the slowest replica connected to the database `conn`
+/// is lagging. The returned value has millisecond precision. If the
+/// database has no replicas, return `0`
+pub(crate) fn replication_lag(conn: &PgConnection) -> Result<Duration, StoreError> {
+    #[derive(Queryable, QueryableByName)]
+    struct Lag {
+        #[sql_type = "Nullable<Integer>"]
+        ms: Option<i32>,
+    }
+
+    let lag = sql_query(
+        "select extract(milliseconds from max(greatest(write_lag, flush_lag, replay_lag)))::int as ms \
+           from pg_stat_replication",
+    )
+    .get_result::<Lag>(conn)?;
+
+    let lag = lag
+        .ms
+        .map(|ms| if ms <= 0 { 0 } else { ms as u64 })
+        .unwrap_or(0);
+
+    Ok(Duration::from_millis(lag))
+}
diff --git a/store/postgres/src/copy.rs b/store/postgres/src/copy.rs
index 6c69664acfb..0d5e2716170 100644
--- a/store/postgres/src/copy.rs
+++ b/store/postgres/src/copy.rs
@@ -38,7 +38,7 @@ use graph::{
 };
 
 use crate::{
-    advisory_lock,
+    advisory_lock, catalog,
     dynds::DataSourcesTable,
     primary::{DeploymentId, Site},
 };
@@ -54,6 +54,16 @@ const INITIAL_BATCH_SIZE_LIST: i64 = 100;
 const TARGET_DURATION: Duration = Duration::from_secs(5 * 60);
 const LOG_INTERVAL: Duration = Duration::from_secs(3 * 60);
 
+/// If replicas are lagging by more than this, the copying code will pause
+/// for a while to allow replicas to catch up
+const MAX_REPLICATION_LAG: Duration = Duration::from_secs(60);
+/// If replicas need to catch up, do not resume copying until the lag is
+/// less than this
+const ACCEPTABLE_REPLICATION_LAG: Duration = Duration::from_secs(30);
+/// When replicas are lagging too much, sleep for this long before checking
+/// the lag again
+const REPLICATION_SLEEP: Duration = Duration::from_secs(30);
+
 table! {
     subgraphs.copy_state(dst) {
         // deployment_schemas.id
@@ -744,6 +754,24 @@ impl Connection {
                 if table.is_cancelled(&self.conn)? {
                     return Ok(Status::Cancelled);
                 }
+
+                // Pause copying if replication is lagging behind to avoid
+                // overloading replicas
+                let mut lag = catalog::replication_lag(&self.conn)?;
+                if lag > MAX_REPLICATION_LAG {
+                    loop {
+                        info!(&self.logger,
+                             "Replicas are lagging too much; pausing copying for {}s to allow them to catch up",
+                             REPLICATION_SLEEP.as_secs();
+                             "lag_s" => lag.as_secs());
+                        std::thread::sleep(REPLICATION_SLEEP);
+                        lag = catalog::replication_lag(&self.conn)?;
+                        if lag <= ACCEPTABLE_REPLICATION_LAG {
+                            break;
+                        }
+                    }
+                }
+
                 let status = self.transaction(|conn| table.copy_batch(conn))?;
                 if status == Status::Cancelled {
                     return Ok(status);