<?xml version="1.0" encoding="US-ASCII"?>
<!-- DFIN New ActiveDisclosure (SM) XBRL Schema Document - http://www.dfinsolutions.com/ -->
<!-- Creation Date :2026-04-10T14:18:21.0281+00:00 -->
<!-- Copyright (c) 2026 Donnelley Financial Solutions, Inc. All Rights Reserved. -->
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  <xsd:import schemaLocation="https://xbrl.sec.gov/ecd/2025/ecd-sub-2025.xsd" namespace="http://xbrl.sec.gov/ecd-sub/2025"/>
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          <link:loc xlink:type="locator" xlink:href="amrn-20260410.xsd#amrn_AaronBergMember" xlink:label="amrn_AaronBergMember"/>
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          <link:loc xlink:type="locator" xlink:href="amrn-20260410.xsd#amrn_KarimMikhailMember" xlink:label="amrn_KarimMikhailMember"/>
          <link:loc xlink:type="locator" xlink:href="amrn-20260410.xsd#amrn_ExclusionOfStockAwardsAndOptionAwardsMember" xlink:label="amrn_ExclusionOfStockAwardsAndOptionAwardsMember"/>
          <link:loc xlink:type="locator" xlink:href="https://xbrl.sec.gov/dei/2025/dei-2025.xsd#dei_EntityRegistrantName" xlink:label="dei_EntityRegistrantName"/>
          <link:loc xlink:type="locator" xlink:href="https://xbrl.sec.gov/dei/2025/dei-2025.xsd#dei_AmendmentDescription" xlink:label="dei_AmendmentDescription"/>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="amrn_ChangeInFairValueFromLastDayOfPriorYearToLastDayOfYearOfUnvestedEquityAwardsMember_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Change in Fair Value from Last Day of Prior Year to Last Day of Year of Unvested Equity Awards [Member]</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="amrn_ChangeInFairValueFromLastDayOfPriorYearToLastDayOfYearOfUnvestedEquityAwardsMember_lbl" xlink:role="http://www.xbrl.org/2003/role/documentation">Change in Fair Value from Last Day of Prior Year to Last Day of Year of Unvested Equity Awards.</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="amrn_ChangeInFairValueFromLastDayOfPriorYearToLastDayOfYearOfUnvestedEquityAwardsMember_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Change in Fair Value from Last Day of Prior Year to Last Day of Year of Unvested Equity Awards [Member]</link:label>
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          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="amrn_VestingDateFairValueOfEquityAwardsGrantedDuringYearThatVestedMember_lbl" xlink:role="http://www.xbrl.org/2003/role/documentation">Vesting-Date Fair Value of Equity Awards Granted During Year that Vested.</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="amrn_VestingDateFairValueOfEquityAwardsGrantedDuringYearThatVestedMember_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Vesting-Date Fair Value of Equity Awards Granted During Year that Vested</link:label>
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          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="dei_DocumentType_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Document Type</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="dei_DocumentType_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Document Type</link:label>
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          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="amrn_ChangeInFairValueFromLastDayOfPriorYearToVestingDateOfUnvestedEquityAwardsThatVestedMember_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Change in Fair Value from Last Day of Prior Year to Vesting Date of Unvested Equity Awards that Vested</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="dei_EntityCentralIndexKey_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">CIK</link:label>
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          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="amrn_PatrickHoltMember_lbl" xlink:role="http://www.xbrl.org/2003/role/documentation">Patrick Holt.</link:label>
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          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="amrn_JohnFTheroMember_lbl" xlink:role="http://www.xbrl.org/2003/role/documentation">John F. Thero.</link:label>
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          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="amrn_AaronBergMember_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Aaron Berg [Member]</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="amrn_AaronBergMember_lbl" xlink:role="http://www.xbrl.org/2003/role/documentation">Aaron Berg [Member]</link:label>
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          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="dei_CoverAbstract_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Cover</link:label>
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</xsd:schema>
