<?xml version="1.0" encoding="UTF-8"?>

<!--XBRL Document Created with the Workiva Platform-->
<!--Copyright 2025 Workiva-->
<!--r:f4c766b6-0bf5-453f-af95-e897415983b8,g:73883bfd-dca5-4557-97db-c9181ae6a043-->
<xs:schema xmlns:xs="http://www.w3.org/2001/XMLSchema" xmlns:link="http://www.xbrl.org/2003/linkbase" xmlns:apog="http://www.apog.com/20250513" xmlns:xbrli="http://www.xbrl.org/2003/instance" xmlns:dtr-types1="http://www.xbrl.org/dtr/type/2020-01-21" attributeFormDefault="unqualified" elementFormDefault="qualified" targetNamespace="http://www.apog.com/20250513">
  <xs:import namespace="http://www.xbrl.org/2003/instance" schemaLocation="http://www.xbrl.org/2003/xbrl-instance-2003-12-31.xsd"/>
  <xs:import namespace="http://www.xbrl.org/2003/linkbase" schemaLocation="http://www.xbrl.org/2003/xbrl-linkbase-2003-12-31.xsd"/>
  <xs:import namespace="http://www.xbrl.org/dtr/type/2020-01-21" schemaLocation="https://www.xbrl.org/dtr/type/2020-01-21/types.xsd"/>
  <xs:import namespace="http://xbrl.sec.gov/dei-sub/2024" schemaLocation="https://xbrl.sec.gov/dei/2024/dei-sub-2024.xsd"/>
  <xs:import namespace="http://xbrl.sec.gov/ecd-sub/2024" schemaLocation="https://xbrl.sec.gov/ecd/2024/ecd-sub-2024.xsd"/>
  <xs:annotation>
    <xs:appinfo>
      <link:linkbaseRef xmlns:xlink="http://www.w3.org/1999/xlink" xlink:arcrole="http://www.w3.org/1999/xlink/properties/linkbase" xlink:href="apog-20250513_pre.xml" xlink:role="http://www.xbrl.org/2003/role/presentationLinkbaseRef" xlink:type="simple"/>
      <link:linkbaseRef xmlns:xlink="http://www.w3.org/1999/xlink" xlink:arcrole="http://www.w3.org/1999/xlink/properties/linkbase" xlink:href="apog-20250513_def.xml" xlink:role="http://www.xbrl.org/2003/role/definitionLinkbaseRef" xlink:type="simple"/>
      <link:linkbaseRef xmlns:xlink="http://www.w3.org/1999/xlink" xlink:arcrole="http://www.w3.org/1999/xlink/properties/linkbase" xlink:href="apog-20250513_lab.xml" xlink:role="http://www.xbrl.org/2003/role/labelLinkbaseRef" xlink:type="simple"/>
    </xs:appinfo>
  </xs:annotation>
  <xs:element id="apog_TyRSilberhornMember" abstract="true" name="TyRSilberhornMember" nillable="true" xbrli:periodType="duration" substitutionGroup="xbrli:item" type="dtr-types1:domainItemType"/>
  <xs:element id="apog_JosephFPuishysMember" abstract="true" name="JosephFPuishysMember" nillable="true" xbrli:periodType="duration" substitutionGroup="xbrli:item" type="dtr-types1:domainItemType"/>
</xs:schema>
